WO2017132905A1 - 控制运动***的方法和装置 - Google Patents

控制运动***的方法和装置 Download PDF

Info

Publication number
WO2017132905A1
WO2017132905A1 PCT/CN2016/073367 CN2016073367W WO2017132905A1 WO 2017132905 A1 WO2017132905 A1 WO 2017132905A1 CN 2016073367 W CN2016073367 W CN 2016073367W WO 2017132905 A1 WO2017132905 A1 WO 2017132905A1
Authority
WO
WIPO (PCT)
Prior art keywords
motion system
motion
determining
constraint
dynamic optimization
Prior art date
Application number
PCT/CN2016/073367
Other languages
English (en)
French (fr)
Inventor
闫正
毕舒展
Original Assignee
华为技术有限公司
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 华为技术有限公司 filed Critical 华为技术有限公司
Priority to PCT/CN2016/073367 priority Critical patent/WO2017132905A1/zh
Publication of WO2017132905A1 publication Critical patent/WO2017132905A1/zh

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls

Definitions

  • the present invention relates to the field of automation technology and, more particularly, to a method and apparatus for controlling a motion system.
  • the motion system consists of a set of rigid segments joined by joints that transform the relative angles and displacements between the joints to produce a specific shape or pose (position and attitude).
  • the inverse kinematic programming problem is the process of determining the motion parameters of the active joint required to achieve a given position and attitude. For example, for a three-dimensional model of a human body, the inverse kinematics plan is how to set the angle of the wrist and elbow so that the hand reaches a waved posture from the relaxed position.
  • a redundant motion system means that the motion system has a greater degree of freedom than the operation (motion) when performing a given task, and has great advantages in complex workspace operations, avoiding obstacles, and optimizing load distribution. Sex.
  • redundant motion systems are highly autonomous, flexible and fault tolerant.
  • such a system loses the joint freedom of the system at a certain attitude, so that the joint degree of freedom is equal to or even less than the degree of freedom of motion, resulting in a singular state, which can make many advantages of the redundant motion system. Lost.
  • the prior art cannot avoid the singular state of the motion system. If the singular state occurs, it can only be solved offline, and the fault tolerance is poor. Moreover, the closed form solution of the inverse kinematics plan can only be obtained by offline operation, and it is difficult to capture the environmental factors of real-time change, and the robustness is poor. In addition, the joint freedom of the joint has a joint limit, and the prior art cannot handle the planning problem in which the joint degree of freedom is constrained.
  • Embodiments of the present invention provide a method and apparatus for controlling a motion system that can prevent a singular state from occurring in a motion system.
  • a method of controlling a motion system comprising:
  • the motion system is controlled based on the motion parameters.
  • the method for controlling a motion system determines a singular constraint condition of the motion system according to an operability index of the motion system, and then dynamically calculates the motion of the motion system according to the dynamic optimization model determined by the singular constraint prevention condition.
  • the parameters can avoid the singular state of the motion system, thus enhancing the fault tolerance of the motion system.
  • the method further includes:
  • the dynamic optimization model of the motion system is determined according to the singular constraint prevention condition, including:
  • the dynamic optimization model of the motion system is determined according to the objective function and the singularity prevention condition.
  • the method further includes:
  • the obstacle avoidance constraint restricting the motion direction of the motion system away from the obstacle when the distance between the motion system and the obstacle tends to the obstacle avoidance distance The direction of the object;
  • the dynamic optimization model of the motion system is determined according to the singular constraint prevention condition, including:
  • the dynamic optimization model of the motion system is determined according to the trajectory tracking constraint condition, the obstacle avoidance constraint condition, the objective function, and the singularity prevention condition.
  • the dynamic optimization model can be determined based on one or more of the above indicators. Of course, it can also be other possible expectations.
  • the dynamic optimization model of the motion system is determined according to the trajectory tracking constraint, the obstacle avoidance constraint, the objective function, and the singularity prevention condition, including:
  • ⁇ represents an infinite norm,
  • the ⁇ is a predetermined threshold greater than 0, the The det represents a matrix determinant, Deriving the derivative
  • determining the motion parameter of the motion system according to the dynamic optimization model includes:
  • the motion parameter of the motion system is determined according to the neural network model corresponding to the dynamic optimization model.
  • the motion system uses the neural network to solve the dynamic optimization model online, so as to obtain the optimal solution of the shutdown degree of freedom, which can avoid offline training without artificial adjustment of internal parameters.
  • determining the motion parameter of the motion system according to the neural network model corresponding to the dynamic optimization model including:
  • the motion parameter is determined according to the following state equation of the neural network model,
  • the ⁇ and the ⁇ are state parameters of the state equation
  • the ⁇ is a gain
  • the g is
  • the J( ⁇ ) T is a transposed matrix of the J( ⁇ )
  • the A is The A T is a transposed matrix of the A
  • the K is an n ⁇ n matrix
  • the kth row and the kth column element of the K matrix are 1 and the remaining elements are all 0, and the b is
  • an apparatus for controlling a motion system for performing the method of any of the above first aspect or any of the possible implementations of the first aspect comprises means for performing the method of any of the above-described first aspect or any of the possible implementations of the first aspect.
  • an apparatus for controlling a motion system includes a processor, a memory, and a communication interface.
  • the processor is coupled to the memory and communication interface.
  • the memory is for storing instructions for the processor to execute, and the communication interface is for communicating with other network elements under the control of the processor.
  • the processor executes the instructions stored by the memory, the execution causes the processor to perform the method of the first aspect or any of the possible implementations of the first aspect.
  • a computer readable medium for storing a computer program comprising instructions for performing the method of the first aspect or any of the possible implementations of the first aspect.
  • Fig. 1 is a structural view showing a mechanical arm to which the technical solution of the embodiment of the present invention can be applied.
  • FIG. 2 shows a schematic flow chart of a method of controlling a motion system in accordance with an embodiment of the present invention.
  • Figure 3 shows a schematic flow chart of a neural network based inverse kinematics plan.
  • Figure 4 shows a simulation result of the motion trajectory of the robot arm.
  • Fig. 5 is a graph showing the simulation results of the velocity information of the joint degrees of freedom of the robot arm.
  • Fig. 6 is a graph showing the simulation results of the manipulator's operability index.
  • Figure 7 shows a schematic block diagram of an apparatus for controlling a motion system in accordance with an embodiment of the present invention.
  • FIG. 8 is a block diagram showing an apparatus for controlling a motion system according to still another embodiment of the present invention.
  • the technical solution of the present invention can be applied to various motion systems, for example, a robot (for example, PUMA560, etc.), an industrial robot arm motion system, a human body three-dimensional model, and the like.
  • a robot for example, PUMA560, etc.
  • the robot performs a specified action by adjusting the angles of the joints of the arm.
  • the angles and angular velocities of the joints of the arm constitute a description of the specific action.
  • the motion of the robot arm is generally described in a state vector in Cartesian coordinate space (such as velocity, displacement, etc. in a plane coordinate system).
  • the position and direction of motion of the robotic arm in a Cartesian coordinate system is called a "positive kinematics problem” or “direct kinematics problem” (ie, motion output and joints) The relationship of degrees of freedom).
  • a positive kinematics problem or "direct kinematics problem” (ie, motion output and joints)
  • the relationship of degrees of freedom During the movement of the arm, it is necessary to constantly change the rotation angle of each joint to reach the corresponding position point.
  • the angle problem between the joints of the corresponding manipulators is solved under the condition of the known trajectory of the manipulator. It is called “inverse kinematics problem” or “reverse kinematics planning problem”.
  • the singular state will cause many advantages of the system to be lost.
  • the present invention proposes a method capable of performing inverse kinematic programming online to prevent singular states.
  • the technical solution of the present invention can be applied to a motion system (for example, a motion system including a robot arm) that involves an inverse kinematics planning problem, which is not limited thereto.
  • the mechanical arm is essentially a motion system with multiple degrees of freedom.
  • FIG. 1 shows a structural view of a mechanical arm to which the technical solution of the embodiment of the present invention can be applied.
  • the robotic arm Mitsubishi PA10-7C
  • the robotic arm mimics the human body structure, including the wrist joint Wrist, the lower arm Lower arm, the elbow joint Elbow, the upper arm Upper arm, and the shoulder Shoulder.
  • the robot arm has seven joint degrees of freedom, and each joint degree of freedom is represented by ⁇ 1 , ⁇ 2 , ... ⁇ 7 , respectively.
  • ⁇ 1 , ⁇ 3 , ⁇ 5 are connected by a rotating shaft, and ⁇ 2 , ⁇ 4 , and ⁇ 6 are connected by a pivot.
  • the degree of freedom of movement of the arm is 3
  • the degree of redundancy ie, joint freedom minus motion freedom
  • the arm is a redundant manipulator.
  • the positive kinematics expression is a characteristic of the system itself, which is obtained according to the spatial physical properties and motion laws of the mechanical arm.
  • FIG. 2 shows a schematic flow diagram of a method 200 of controlling a motion system in accordance with an embodiment of the present invention.
  • the motion system can be the robot arm of Figure 1 above.
  • the method 200 can be performed by the robotic arm described above. As shown in FIG. 2, the method 200 includes:
  • S220 Determine a dynamic optimization model of the motion system according to the singular constraint prevention condition
  • the method for controlling a motion system determines a singular constraint condition for preventing a singular constraint condition of the motion system according to an operability of the motion system when performing inverse kinematics planning.
  • the value of the operability of the motion system is greater than 0, and the dynamic optimization model of the motion system is determined according to the singular constraint prevention condition.
  • the dynamic optimization model is solved, and the motion parameter of the motion system can be obtained, and the motion parameter represents the specified pose
  • the angle value between the joints of the corresponding mechanical arm the motion system controls the motion system to achieve the specified posture according to the motion parameter.
  • the singular constraint is prevented from being used to prevent the singular state from occurring in the motion system.
  • the motion system produces a singular state.
  • the singularity constraint prevention condition of the embodiment of the present invention is expressed as forcing the value of the operability to be greater than 0, thereby ensuring that the motion system avoids the occurrence of singular states during the motion.
  • operability is an indicator of the motion system, similar to energy, speed, and the like.
  • the operability of a motion system can be passed through a formula Characterization, M( ⁇ ) represents the value of operability, det represents the matrix determinant, and J( ⁇ ) represents the Jacobian matrix.
  • M( ⁇ ) the value of operability
  • det the matrix determinant
  • J( ⁇ ) the Jacobian matrix
  • the threshold can be customized to force the value of the operability to be greater than the custom threshold to prevent the motion system from being singular.
  • the singularity constraint can be passed through a formula To characterize, where ⁇ denotes a gradient operator, The ⁇ is a user-defined predetermined threshold greater than zero.
  • the dynamic optimization model may consider a plurality of expected indicators, for example, in the robot path planning, by comprehensively considering joint limits of joint degrees of freedom, avoiding obstacles, avoiding singular states, and optimizing paths, etc. Dynamic optimization model.
  • the method for controlling the motion system determines the singular constraint condition of the motion system according to the operability index of the motion system, and then solves the motion system online according to the dynamic optimization model determined by the singular constraint prevention condition.
  • the motion parameters can avoid the singular state of the motion system, thus enhancing the fault tolerance of the motion system.
  • the number of performance indicators of the dynamic optimization model is not limited, and one or more performance indicators may be considered to establish a dynamic optimization model.
  • the method 200 further includes:
  • the dynamic optimization model of the motion system is determined according to the singular constraint prevention condition, including:
  • the dynamic optimization model of the motion system is determined according to the objective function and the singularity prevention condition.
  • the energy index of the motion system can be the minimum energy indicator, that is, the motion system should complete the given task with as little energy as possible;
  • the speed index can be the minimum joint speed, and the smaller joint speed can make the motion system have more Good maneuverability.
  • the motion system can determine the objective function, and combined with the prevention of singular constraints, construct a dynamic optimization model of the constrained motion system, that is, the dynamic optimization problem of multi-objective inverse kinematics planning, An optimal solution can be obtained under a plurality of conditions satisfying the minimum energy, the minimum joint speed, and the prevention of singularity, and the control of the motion system is completed according to the optimal solution.
  • the method 200 further includes:
  • the obstacle avoidance constraint restricting the motion direction of the motion system away from the obstacle when the distance between the motion system and the obstacle tends to the obstacle avoidance distance The direction of the object;
  • the dynamic optimization model of the motion system is determined according to the singular constraint prevention condition, including:
  • the dynamic optimization model of the motion system is determined according to the trajectory tracking constraint condition, the obstacle avoidance constraint condition, the objective function, and the singularity prevention condition.
  • the motion system needs to complete a specified task when moving, that is, tracking a specified motion reference trajectory, and determining a trajectory tracking constraint according to the motion reference trajectory.
  • the motion system should also have the ability to automatically avoid obstacles.
  • the specific performance is to determine the obstacle avoidance constraint according to the obstacle avoidance safety distance of the motion system.
  • the obstacle avoidance constraint is used to constrain the motion direction. When the distance between the motion system and the obstacle tends to avoid the obstacle, the distance is away from the obstacle.
  • the motion system Based on the trajectory tracking constraint condition and the obstacle avoidance constraint condition, the motion system combines the above objective function and the singular constraint prevention condition to construct the dynamic optimization model of the constrained motion system, that is, the dynamic optimization of multi-objective inverse kinematics planning.
  • the problem is that an optimal solution can be obtained under a plurality of conditions satisfying minimum energy, minimum joint velocity, tracking motion reference trajectory, avoiding obstacles, and preventing singularity, and completing control of the motion system according to the optimal solution.
  • determining the dynamic optimization model of the motion system according to the trajectory tracking constraint condition, the obstacle avoidance constraint condition, the objective function, and the singularity prevention condition including:
  • the dynamic optimization model is determined according to the following formula (1),
  • ⁇ represents an infinite norm,
  • the ⁇ is a predetermined threshold greater than 0, the The det represents a matrix determinant, Deriving the derivative
  • a continuous time dynamic optimization model is constructed to represent the inverse kinematic programming problem with redundancy.
  • the inverse kinematic programming problem uses the derivative of the joint degree of freedom (ie, the velocity variable) as the decision variable, and the sum of the two norms and the infinite norm of the derivative of the joint degree of freedom is the objective function, and the trajectory tracking is the equality constraint.
  • the obstacle avoidance and the prevention of singularity are inequality constraints, so that the optimal solution, that is, the motion parameters obtained from the inverse kinematics planning problem, realizes the control of the motion system.
  • a representation method for preventing singular degrees of freedom is proposed for the first time, that is, among them,
  • the det represents a matrix determinant, and ⁇ >0, which is a custom threshold.
  • determining the motion parameter of the motion system according to the dynamic optimization model includes:
  • the motion parameter of the motion system is determined according to the neural network model corresponding to the dynamic optimization model.
  • the dynamic optimization problem needs to be solved, and the dynamic optimization model is solved online by using the neural network to obtain the motion parameters of the motion system.
  • the neural network is introduced online to avoid complex parameterization and derivation processes.
  • the neural network model has a simple structure and does not require manual adjustment of internal parameters.
  • determining the motion parameter of the motion system according to the neural network model corresponding to the dynamic optimization model including:
  • the motion parameter is determined according to the state equation of the neural network model of the following formula (2),
  • the ⁇ and the ⁇ are state parameters of the state equation
  • the ⁇ is a gain
  • the g is
  • the J( ⁇ ) T is a transposed matrix of the J( ⁇ )
  • the A is The A T is a transposed matrix of the A
  • the K is an n ⁇ n matrix
  • the kth row and the kth column element of the K matrix are 1 and the remaining elements are all 0, and the b is
  • a neural network model can be designed to calculate the global optimal solution of the equation (1) in real time.
  • the equation (2) is obtained as the state equation of the neural network, wherein ⁇ in the equation (2) is a sufficiently large gain, and the g is Incentive function,
  • ⁇ in the equation (2) is a sufficiently large gain
  • g is Incentive function
  • Figure 3 shows a schematic flow chart of a neural network based inverse kinematics plan. It should be noted that this is only to assist those skilled in the art to better understand the embodiments of the present invention and not to limit the scope of the embodiments of the present invention.
  • a corresponding Jacobian matrix is obtained according to its known positive kinematics expression, and multiple singularities, desired poses, obstacle avoidance indicators, etc. of the motion system are considered.
  • the expected index is obtained by multi-objective inverse motion planning description, that is, the dynamic optimization model.
  • the dynamic optimization model is substituted into the neural network model, and the state equation corresponding to the neural network model is solved to obtain the optimal joint speed. And joint freedom degrees ⁇ , which are fed back to the motion system so that the motion system operates at the optimal joint speed or joint freedom.
  • the embodiment of the invention uses the neural network to optimize the inverse kinematic programming problem online, avoids the complicated parameterized transportation and derivation process, and can output the optimal degree of freedom velocity information of the inverse kinematic programming problem in real time through the neural network.
  • the modeling process of the neural network model can be referred to the prior art, and will not be described here.
  • the state equation of the neural network describes the model and learning rules of the neural network, which can be understood as a functional module, and its physical implementation may be a neuromorphic chip, a digital signal processor (Digital Signal Processor, referred to as "DSP"). ), software simulation, etc., the present invention Not limited.
  • DSP Digital Signal Processor
  • the method for controlling the motion system determines the singularity constraint condition of the motion system according to the operability index of the motion system, and then determines the dynamic optimization model according to the singular constraint prevention condition and other multiple performance indicators. Further, the motion parameters of the motion system are solved online by the neural network, and offline training is not needed, which can avoid the singular state of the motion system, thereby enhancing the fault tolerance of the motion system.
  • the end manipulator of the manipulator is to perform a circular operation with a radius of 20 cm in the operating space, and to avoid two obstacles in the operating space, that is, any part of the manipulator is required to be 5 cm away from any obstacle. .
  • the spatial position coordinates of the two obstacles are (0, -0.2, 1) and (-0.1, 0.1, 0.8), respectively.
  • the speed of each joint degree of freedom of the arm is constrained The absolute value must be less than 1 rad/s.
  • the motion reference trajectory of the circumferential operation with the above radius of 20 cm is as shown in the following formula (3):
  • x 0 , y 0 , and z 0 are initial states of the robot arm in a Cartesian coordinate system.
  • the degrees of freedom of the joints of the above-mentioned robot arms are solved, and the specific implementation is as follows:
  • Adopt speed information Describe the various indicators that the robotic arm expects in the inverse kinematics plan:
  • OC (OC 1 ; OC 2 ), OC 1 is calculated from the projection vector of the first obstacle (0, -0.2, 1) to the arm, and the second obstacle of OC 2 (-0.1 , 0.1, 0.8) is obtained by calculating the projection vector of the manipulator.
  • the symbolic expression of J c ( ⁇ ) is the same as J( ⁇ ); preventing the use of singular constraints Said that Det represents a matrix determinant;
  • the For the upper limit of ⁇ the For the lower limit ⁇ min of ⁇ , here Is -1rad/s, It is 1 rad/s.
  • the neural network-based inverse kinematics planning method of the manipulator in this example is given in 1) to 4) above.
  • the method can be verified by simulation.
  • it can be used in VC6.0 (ie Microsoft Visual C++ 6.0) environment.
  • VC6.0 ie Microsoft Visual C++ 6.0
  • Matlab environment programming simulation is used to implement the inverse kinematics planning method, which is not limited.
  • Figure 4 shows a simulation result of the motion trajectory of the robot arm.
  • the three axes of the operating space of the arm movement path are the x-axis (m), the y-axis (m), and the z-axis (m), respectively.
  • the two black points correspond to the spatial coordinates (0, -0.2, 1) and (-0.1, 0.1, 0.8) of the obstacle, respectively.
  • Simulation results It shows that the robot arm can complete the required circular operation with a radius of 20 cm, and there is no collision obstacle during the movement, and no singular state is generated.
  • the generation of singularity can be understood as the fact that the two rods coincide in a straight line, that is, one degree of freedom is lost.
  • Fig. 5 is a graph showing the simulation results of the velocity information of the joint degrees of freedom of the robot arm.
  • the horizontal axis t is time (s) and the longitudinal axis joint velocity (rad/s), and the seven lines in the figure represent velocity information of seven joint degrees of freedom, respectively.
  • the simulation results show that the speed of the seven joint degrees of freedom during the movement
  • the absolute value is controlled at 1 rad/s at any time. Among them, there is a joint that does not need to move, that is, its output value coincides with the x-axis.
  • Fig. 6 is a graph showing the simulation results of the manipulator's operability index.
  • the horizontal axis t is time (s)
  • the vertical axis M represents an operability index, that is, the constraint-preventing singular condition of the embodiment of the present invention
  • the simulation result 1 in the figure is the operability index of the present invention.
  • the simulation result 2 is an operability index which does not employ the technical solution of the present invention.
  • the simulation results show that if the technical solution of the present invention is not adopted, in the 4th to 6s motion interval, the simulation result 2 has a singular state, and the value of the operability index tends to 0, and the technical solution of the present invention is used for simulation. As a result, the singular state does not occur, thereby embodying the superiority of the technical solution of the present invention.
  • the mechanical arm determines a dynamic optimization model according to a plurality of performance indicators, the performance indicators include minimum energy, minimum speed, trajectory tracking, prevention of singularity, and avoidance of obstacles.
  • the dynamic optimization is solved online by using a neural network. The model obtains the optimal numerical solution of the seven joint degrees of freedom of the robot arm, eliminating the need for off-line training, and avoiding the singular state of the robot arm, thereby enhancing the fault tolerance of the system.
  • the size of the sequence numbers of the above processes does not mean the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not be directed to the embodiments of the present invention.
  • the implementation process constitutes any limitation.
  • a method of controlling a motion system according to an embodiment of the present invention is described in detail above, and an apparatus for controlling a motion system according to an embodiment of the present invention will be described below.
  • FIG. 7 shows a schematic block diagram of an apparatus 700 for controlling a motion system in accordance with an embodiment of the present invention. As shown in FIG. 7, the apparatus 700 includes:
  • a determining module 710 configured to determine, according to the operability index of the motion system, a singular constraint condition of the motion system, the singular constraint condition limiting the operability of the motion system is greater than 0;
  • the optimization module 720 is configured to determine, according to the determining module 710, the singularity constraint Determining the dynamic optimization model of the motion system;
  • the processing module 730 is configured to determine a motion parameter of the motion system according to the dynamic optimization model determined by the optimization module 720;
  • the control module 740 is configured to control the motion system according to the motion parameter determined by the processing module 730.
  • the method for controlling a motion system determines a singular constraint condition of the motion system according to an operability index of the motion system, and then dynamically calculates the motion of the motion system according to the dynamic optimization model determined by the singular constraint prevention condition.
  • the parameters can avoid the singular state of the motion system, thus enhancing the fault tolerance of the motion system.
  • the determining module 710 is further configured to determine an objective function according to the energy indicator and the speed indicator of the motion system;
  • the optimization module 720 is specifically configured to:
  • the dynamic optimization model of the motion system is determined according to the objective function determined by the determining module 710 and the singularity prevention condition.
  • the determining module 710 is further configured to determine a trajectory tracking constraint according to the motion reference trajectory of the motion system
  • the determining module 710 is further configured to determine an obstacle avoidance constraint according to the obstacle avoidance safety distance of the motion system, the obstacle avoidance constraint restricting a motion direction of the motion system, and a distance between the motion system and the obstacle tends to avoid the obstacle
  • the safety distance is the direction away from the obstacle
  • the optimization module 720 is specifically configured to:
  • the dynamic optimization model of the motion system is determined according to the trajectory tracking constraint condition, the obstacle avoidance constraint condition, the objective function, and the singularity prevention condition.
  • the optimization module 720 is specifically configured to:
  • 2 represents a two norm
  • ⁇ represents an infinite norm
  • the ⁇ is a predetermined threshold greater than 0, the The det represents a matrix determinant, Deriving the
  • processing module 730 is specifically configured to:
  • the motion parameter of the motion system is determined according to the neural network model corresponding to the dynamic optimization model.
  • processing module 730 is specifically configured to:
  • the motion parameter is determined according to the following state equation of the neural network model,
  • the ⁇ and the ⁇ are state parameters of the state equation
  • the ⁇ is a gain
  • the g is
  • the J( ⁇ ) T is a transposed matrix of the J( ⁇ )
  • the A is The A T is a transposed matrix of the A
  • the K is an n ⁇ n matrix
  • the kth row and the kth column element of the K matrix are 1 and the remaining elements are all 0, and the b is
  • the device for controlling the motion system determines the singular constraint condition of the motion system according to the operability index of the motion system, and then determines the dynamic optimization model according to the singular constraint prevention condition and other multiple performance indicators. Further, the motion parameters of the motion system are solved online by using a neural network, and offline training is not required, and the singularity of the motion system can be avoided. State, thus enhancing the fault tolerance of the motion system.
  • Apparatus 700 for controlling a motion system in accordance with an embodiment of the present invention may perform a method of controlling a motion system in accordance with an embodiment of the present invention, and the above and other operations and/or functions of the various modules in the apparatus 700 are respectively implemented to implement the various methods described above.
  • the corresponding process, for the sake of brevity, will not be described here.
  • FIG. 8 shows a structure of an apparatus for controlling a motion system according to still another embodiment of the present invention, comprising at least one processor 802 (for example, a CPU), at least one network interface 805 or other communication interface, a memory 806, and at least one communication.
  • a bus 803 is used to implement connection communication between these devices.
  • the processor 802 is configured to execute executable modules, such as computer programs, stored in the memory 806.
  • the memory 806 may include a high speed random access memory (RAM: Random Access Memory), and may also include a non-volatile memory such as at least one disk memory.
  • a communication connection with at least one other network element is achieved by at least one network interface 805 (which may be wired or wireless).
  • the memory 806 stores a program 8061
  • the processor 802 executes the program 8061 for performing the method of controlling the motion system of the aforementioned embodiment of the present invention.
  • the size of the sequence numbers of the above processes does not mean the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not be directed to the embodiments of the present invention.
  • the implementation process constitutes any limitation.
  • the disclosed systems, devices, and methods may be implemented in other manners.
  • the device embodiments described above are merely illustrative
  • the division of the unit is only a logical function division, and the actual implementation may have another division manner, for example, multiple units or components may be combined or may be integrated into another system, or some features may be Ignore, or not execute.
  • the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, and may be in an electrical, mechanical or other form.
  • the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of the embodiment.
  • each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
  • the functions may be stored in a computer readable storage medium if implemented in the form of a software functional unit and sold or used as a standalone product.
  • the technical solution of the present invention which is essential or contributes to the prior art, or a part of the technical solution, may be embodied in the form of a software product, which is stored in a storage medium, including
  • the instructions are used to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention.
  • the foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and the like. .

Landscapes

  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Manipulator (AREA)

Abstract

一种控制运动***的方法和装置（700），该方法包括：根据该运动***的可操作性指标，确定该运动***的防止奇异约束条件，该防止奇异约束条件约束该运动***的可操作性的值大于0（S210）；根据该防止奇异约束条件确定该运动***的动态优化模型（S220）；根据该动态优化模型确定该运动***的运动参数（S230）；根据该运动参数控制该运动***（S240）。该控制运动***的方法和装置（700）能够避免运动***发生奇异状态。

Description

控制运动***的方法和装置 技术领域
本发明涉及自动化技术领域，并且更具体地，涉及控制运动***的方法和装置。
背景技术
运动***由一组通过关节连接的刚性片段组成，变换各个关节之间的相对角度和位移可以产生特定的形状或位姿(位置和姿态)。在运动***中，逆运动学规划问题即决定要达成给定的位置和姿态所需要的活动关节的运动参数的过程。例如，对于一个人体的三维模型，逆运动学规划即如何设置手腕和手肘的角度使得手从放松位置达成挥手的姿势。具有冗余度的运动***是指运动***在执行给定的任务时其关节自由度大于操作(运动)自由度，在复杂工作空间作业、躲避障碍物、优化载荷分配等方面具有很大的优越性。在实际应用中，具有冗余度的运动***有高度的自治性、灵活性和容错性。但是，此类***在某个特定的姿态会损失***的关节自由度，使得关节自由度等于甚至小于运动自由度，从而造成奇异状态，发生奇异状态会使得具有冗余度的运动***的诸多优势丧失。
现有技术不能避免运动***出现奇异状态，如果出现奇异状态时，只能离线重新求解，容错性较差。并且，只能通过离线运算获取逆运动学规划的闭形式解，难以捕捉实时变化的环境因素，鲁棒性较差。另外，一般的关节自由度都存在关节极限，现有技术也不能处理关节自由度有约束的规划问题。
发明内容
本发明实施例提供了一种控制运动***的方法和装置，能够避免运动***发生奇异状态。
第一方面，提供了一种控制运动***的方法，包括：
根据该运动***的可操作性指标，确定该运动***的防止奇异约束条件，该防止奇异约束条件约束该运动***的可操作性的值大于0；
根据该防止奇异约束条件确定该运动***的动态优化模型；
根据该动态优化模型确定该运动***的运动参数；
根据该运动参数控制该运动***。
本发明实施例的控制运动***的方法，根据运动***的可操作性指标，确定该运动***的防止奇异约束条件，再根据该防止奇异约束条件确定的动态优化模型在线求解出该运动***的运动参数，能够避免运动***发生奇异状态，从而增强了运动***的容错性。
在一些可能的实现方式中，该方法还包括：
根据该运动***的能量指标和速度指标，确定目标函数；
其中，该根据该防止奇异约束条件确定该运动***的动态优化模型，包括：
根据该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
在一些可能的实现方式中，该方法还包括：
根据该运动***的运动参考轨迹，确定轨迹追踪约束条件；
根据该运动***的避障安全距离，确定避障约束条件，该避障约束条件约束该运动***的运动方向在该运动***与该障碍物的距离趋于该避障安全距离时为远离该障碍物的方向；
其中，该根据该防止奇异约束条件确定该运动***的动态优化模型，包括：
根据该轨迹追踪约束条件、该避障约束条件、该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
这里，动态优化模型可以根据上述一个或多个指标进行确定。当然，也可以是其他可能的期望指标。
在一些可能的实现方式中，该根据该轨迹追踪约束条件、该避障约束条件、该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型，包括：
根据下列公式确定该动态优化模型，
Figure PCTCN2016073367-appb-000001
其中，该运动***为n个关节自由度θ＝(θ1,θ2,...θn)的运动***，该
Figure PCTCN2016073367-appb-000002
为该θ对时间t求导的导数的二范数的平方，该||·||2表示二范数，该
Figure PCTCN2016073367-appb-000003
为该θ对该t求导的导数的无穷范数的平方，该||·||∞表示无穷范数，该
Figure PCTCN2016073367-appb-000004
为该目标函数，该
Figure PCTCN2016073367-appb-000005
为该轨迹追踪约束条件，该
Figure PCTCN2016073367-appb-000006
为该运动***的正运动学表达式r＝f(θ)对该t求导的表达式，该J(θ)为该f(θ)的雅可比矩阵，该
Figure PCTCN2016073367-appb-000007
为该避障约束条件，该
Figure PCTCN2016073367-appb-000008
是由障碍物O指向运动关节C的向量，该Jc(θ)为所述运动关节C对应的雅可比矩阵，该
Figure PCTCN2016073367-appb-000009
为该防止奇异约束条件，该
Figure PCTCN2016073367-appb-000010
该δ为大于0的预定阈值，该
Figure PCTCN2016073367-appb-000011
该det表示矩阵行列式，该
Figure PCTCN2016073367-appb-000012
为该θ的上限θmax对该t求导的导数，该
Figure PCTCN2016073367-appb-000013
为该θ的下限θmin对该t求导的导数。
在一些可能的实现方式中，该根据该动态优化模型，确定该运动***的该运动参数包括：
根据该动态优化模型对应的神经网络模型，确定该运动***的该运动参数。
这里，运动***在得到动态优化模型后，采用神经网络对该动态优化模型进行在线求解，从而得到关机自由度的最优解，能够避免离线训练，无需人为调整内部参数。
在一些可能的实现方式中，该根据该动态优化模型对应的神经网络模型，确定该运动***的该运动参数，包括：
根据以下该神经网模型的状态方程确定该运动参数，
Figure PCTCN2016073367-appb-000014
其中，该μ和该ρ均为该状态方程的状态参数，该ε为增益，该g为
Figure PCTCN2016073367-appb-000015
该J(θ)T为该J(θ)的转置矩阵，该A为
Figure PCTCN2016073367-appb-000016
该AT为该A的转置矩阵，该K为n×n矩阵，且该K矩阵的第k行第k列元素为1其余元素均为0，该b为
Figure PCTCN2016073367-appb-000017
第二方面，提供了一种控制运动***的装置，用于执行上述第一方面或第一方面的任意可能的实现方式中的方法。具体地，该装置包括用于执行上述第一方面或第一方面的任意可能的实现方式中的方法的单元。
第三方面，提供了一种控制运动***的装置。该装置包括处理器、存储器和通信接口。处理器与存储器和通信接口连接。存储器用于存储指令，处理器用于执行该指令，通信接口用于在处理器的控制下与其他网元进行通信。该处理器执行该存储器存储的指令时，该执行使得该处理器执行第一方面或第一方面的任意可能的实现方式中的方法。
第四方面，提供了一种计算机可读介质，用于存储计算机程序，该计算机程序包括用于执行第一方面或第一方面的任意可能的实现方式中的方法的指令。
附图说明
为了更清楚地说明本发明实施例的技术方案，下面将对本发明实施例中所需要使用的附图作简单地介绍，显而易见地，下面所描述的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1示出了可应用本发明实施例的技术方案的机械臂的结构图。
图2示出了根据本发明实施例的控制运动***的方法的示意性流程图。
图3示出了基于神经网络的逆运动学规划的示意性流程图。
图4示出了机械臂的运动轨迹仿真结果图。
图5示出了机械臂的关节自由度的速度信息仿真结果图。
图6示出了机械臂的可操作性指数仿真结果图。
图7示出了根据本发明实施例的控制运动***的装置的示意性框图。
图8示出了本发明的又一实施例提供的控制运动***的装置的结构图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明的技术方案，可以应用于各种运动***中，例如，机器人(例如PUMA560等)、工业机械臂运动***、人体三维模型等。以机器人为例，通常，机器人完成某一指定动作是通过调节机械臂各个关节的角度来实现的，机械臂各个关节的角度及角速度构成了特定动作的一种描述。机械臂的动作一般以笛卡尔坐标空间中的状态向量(如平面坐标系中的速度、位移等)来描述。例如，对于给定的一组机械臂关节间的角度，机械臂在笛卡尔坐标系中的位置及运动方向称为“正运动学问题”或“直接运动学问题”(即运动输出与各关节自由度的关系)。在机械臂运动过程中，需要不断变换各个关节的旋转角度，从而到达相应的位置点。为了控制机械臂的运动，在已知机械臂的运动轨迹条件下，求解对应的机械臂关节间的角度问题。则称为“逆运动学问题”或“逆运动学规划问题”。通常来讲，具有冗余度的机械臂或运动***中，发生奇异状态后会使得***的诸多优势丧失。为了解决这个问题，本发明提出了一种能够在线进行逆运动学规划的方法，以防止奇异状态。
应理解，对于涉及到逆运动学规划问题的运动***(例如包含机械臂的运动***)，都可以应用本发明的技术方案，对此不作限定。其中，机械臂本质上也是一个具有多自由度的运动***。
例如，图1示出了可应用本发明实施例的技术方案的机械臂的结构图。应理解，这里仅以图1为例，但并不构成对本发明的限制。如图1所示，该机械臂(Mitsubishi PA10-7C)结构模仿人体结构，包括腕关节Wrist、下臂Lower arm、肘关节Elbow、上臂Upper arm和肩部Shoulder。该机械臂具有 7个关节自由度，每个关节自由度分别用θ1,θ2,...θ7表示。其中，θ1,θ3,θ5是通过旋转轴连接，θ2,θ4,θ6是通过枢轴连接。如果只考虑操作器位置移动的情况下，该机械臂的运动自由度为3，冗余度(即关节自由度减运动自由度)为4，则该机械臂为具有冗余度的机械臂。该机械臂的正运动学表达式为r＝f(θ)。该正运动学表达式是***本身的特性，是根据机械臂的空间物理性质和运动规律所得。
图2示出了根据本发明实施例的控制运动***的方法200的示意性流程图。该运动***可以为上述图1中的机械臂。该方法200可以由上述机械臂执行。如图2所示，该方法200包括：
S210，根据该运动***的可操作性指标，确定该运动***的防止奇异约束条件，该防止奇异约束条件约束该运动***的可操作性的值大于0；
S220，根据该防止奇异约束条件确定该运动***的动态优化模型；
S230，根据该动态优化模型确定该运动***的运动参数；
S240，根据该运动参数控制该运动***。
具体而言，本发明实施例的控制运动***的方法，在进行逆运动学规划时，根据该运动***的可操作性这一指标，确定该运动***的防止奇异约束条件，该防止奇异约束条件约束该运动***的可操作性的值大于0，根据该防止奇异约束条件确定该运动***的动态优化模型，对该动态优化模型求解，可以得到运动***的运动参数，该运动参数表征指定位姿时对应的机械臂关节间的角度值，运动***根据该运动参数控制运动***达成指定位姿。
在本发明实施例中，防止奇异约束条件是用于防止运动***发生奇异状态。当可操作性的值为0时，运动***会产生奇异状态。本发明实施例的防止奇异约束条件表示为强制该可操作性的值大于0，从而保证运动***在运动过程中避免发生奇异状态。
在本发明实施例中，可操作性为运动***的一个指标，类似于能量、速度等。例如，运动***的可操作性可通过公式
Figure PCTCN2016073367-appb-000018
表征，M(θ)表示可操作性的值，det表示矩阵行列式，J(θ)表示雅可比矩阵。这里，当可操作性的值M(θ)＝0时，运动***产生奇异状态。为了防止运动***奇异，需要强制该可操作性的值大于0，本发明引入所述防止奇异约束条件来解决该问题。所述防止奇异约束条件具体的实现方法是，对M(θ)按照时间进行求导，当可操作性的值趋于0时，强制其导数为非负值，这样使得可操作数值不再下降，呈上升趋势，从而使得M(θ)＞0，即
Figure PCTCN2016073367-appb-000019
进一步地，可以自定义阈值，强制可操作性的值大于该自定义阈值，以防止运动***发生奇异。例如，该防止奇异约束条件可通过公式
Figure PCTCN2016073367-appb-000020
来表征，其中，▽表示梯度算子，
Figure PCTCN2016073367-appb-000021
该δ为用户自定义的大于0的预定阈值。
可选地，该动态优化模型可以考虑多个期望指标，例如，在机器人路径规划中，通过综合考虑关节自由度的关节极限、躲避障碍物、避免发生奇异状态、路径最优等多个性能指标建立动态优化模型。
因此，本发明实施例的控制运动***的方法，根据运动***的可操作性指标，确定该运动***的防止奇异约束条件，再根据该防止奇异约束条件确定的动态优化模型在线求解出该运动***的运动参数，能够避免运动***发生奇异状态，从而增强了运动***的容错性。
应理解，在本发明实施例中，对该动态优化模型的性能指标的数目不作限制，可以考虑一个或多个性能指标建立动态优化模型。
例如，可选地，该方法200还包括：
根据该运动***的能量指标和速度指标，确定目标函数；
其中，该根据该防止奇异约束条件确定该运动***的动态优化模型，包括：
根据该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
具体而言，运动***的能量指标可以是能量最小指标，即运动***应该以尽可能小的能量完成给定的任务；速度指标可以是关节速度最小，较小的关节速度可以使得运动***具有更好的可操控性。运动***通过该能量指标和该速度指标可以确定出目标函数，同时结合防止奇异约束条件，构造出带有约束的运动***的动态优化模型，即多目标下逆运动学规划的动态优化问题，从而可得到在满足能量最小、关节速度最小以及防止奇异的多个条件下的最优解，根据最优解完成对运动***的控制。
又例如，可选地，该方法200还包括：
根据该运动***的运动参考轨迹，确定轨迹追踪约束条件；
根据该运动***的避障安全距离，确定避障约束条件，该避障约束条件约束该运动***的运动方向在该运动***与该障碍物的距离趋于该避障安全距离时为远离该障碍物的方向；
其中，该根据该防止奇异约束条件确定该运动***的动态优化模型，包括：
根据该轨迹追踪约束条件、该避障约束条件、该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
具体而言，运动***在运动时需要完成指定的任务，即跟踪指定的运动参考轨迹，根据该运动参考轨迹确定轨迹追踪约束条件。另外，在工作空间内存在障碍物时，运动***还应具有自动避障的能力，具体表现为根据运动***的避障安全距离，确定避障约束条件，该避障约束条件用于约束运动方向在运动***与障碍物的距离趋于避障安全距离时为远离障碍物的方向。运动***根据该轨迹追踪约束条件、该避障约束条件，同时结合上述目标函数和防止奇异约束条件，构造出带有约束的运动***的动态优化模型，即多目标下逆运动学规划的动态优化问题，从而可得到在满足能量最小、关节速度最小、跟踪运动参考轨迹、躲避障碍物以及防止奇异的多个条件下的最优解，根据最优解完成对运动***的控制。
可选地，该根据该轨迹追踪约束条件、该避障约束条件、该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型，包括：
根据下列公式(1)确定该动态优化模型，
Figure PCTCN2016073367-appb-000022
其中，该运动***为n个关节自由度θ＝(θ1,θ2,...θn)的运动***，该
Figure PCTCN2016073367-appb-000023
为该θ对时间t求导的导数的二范数的平方，该||·||2表示二范数，该
Figure PCTCN2016073367-appb-000024
为该θ对该t求导的导数的无穷范数的平方，该||·||∞表示无穷范数，该
Figure PCTCN2016073367-appb-000025
为该目标函数，该
Figure PCTCN2016073367-appb-000026
为该轨迹追踪约束条件，该
Figure PCTCN2016073367-appb-000027
为该运动***的正运动学表达式r＝f(θ)对该t求导的表达式，该J(θ)为该f(θ)的雅可比矩阵，该
Figure PCTCN2016073367-appb-000028
为该避障约束条件，该
Figure PCTCN2016073367-appb-000029
是由障碍物O指向运动关节C的向量，该Jc(θ)为所述运动关节C对应的雅可比矩阵，该
Figure PCTCN2016073367-appb-000030
为该防止奇异约束条件， 该
Figure PCTCN2016073367-appb-000031
该δ为大于0的预定阈值，该
Figure PCTCN2016073367-appb-000032
该det表示矩阵行列式，该
Figure PCTCN2016073367-appb-000033
为该θ的上限θmax对该t求导的导数，该
Figure PCTCN2016073367-appb-000034
为该θ的下限θmin对该t求导的导数。这里，
Figure PCTCN2016073367-appb-000035
可以表示能量最小，
Figure PCTCN2016073367-appb-000036
可以表示速度最小。
在本发明实施例中，构造了一个连续时间的动态优化模型来表示具有冗余度的逆运动学规划问题。该逆运动学规划问题采用关节自由度的导数(即速度变量)为决策变量，以该关节自由度的导数的二范数和无穷范数的和为目标函数，以轨迹追踪为等式约束，以避障和防止奇异为不等式约束，从而根据该逆运动学规划问题得到的最优解即运动参数，实现对运动***的控制。
在本发明实施例中，首次提出一种防止奇异的自由度的表示方法，即
Figure PCTCN2016073367-appb-000037
其中，
Figure PCTCN2016073367-appb-000038
该det表示矩阵行列式，该δ＞0，为自定义的阈值。
可选地，作为一个实施例，该根据该动态优化模型，确定该运动***的该运动参数包括：
根据该动态优化模型对应的神经网络模型，确定该运动***的该运动参数。
具体而言，在得到动态优化模型后，需要对动态优化问题进行求解，采用神经网络对该动态优化模型进行在线求解，得到运动***的运动参数。这里引入神经网络在线求解，避免了复杂的参数化运算和推导过程，并且，神经网络模型结构简单，无需人为调整内部参数。
可选地，该根据该动态优化模型对应的神经网络模型，确定该运动***的该运动参数，包括：
根据以下式(2)该神经网模型的状态方程确定该运动参数，
Figure PCTCN2016073367-appb-000039
其中，该μ和该ρ均为该状态方程的状态参数，该ε为增益，该g为
Figure PCTCN2016073367-appb-000040
该J(θ)T为该J(θ)的转置矩阵，该A为
Figure PCTCN2016073367-appb-000041
该AT为该A的转置矩阵，该K为n×n矩阵，且该K矩阵的第k行第k列元素为1其余元素均为0，该b为
Figure PCTCN2016073367-appb-000042
具体而言，对于动态优化模型式(1)可以设计一个神经网络模型，实时计算该式(1)的全局最优解。根据式(1)定义
Figure PCTCN2016073367-appb-000043
Figure PCTCN2016073367-appb-000044
得到式(2)即为神经网络的状态方程，其中，式(2)中的ε为一个足够大的增益，该g为
Figure PCTCN2016073367-appb-000045
的激励函数，
Figure PCTCN2016073367-appb-000046
为n维的向量，假设
Figure PCTCN2016073367-appb-000047
是n维向量
Figure PCTCN2016073367-appb-000048
中绝对值数值最大的元素，即
Figure PCTCN2016073367-appb-000049
定义K为n×n矩阵，且该K矩阵的第k行第k列元素为1其余元素均为0。
图3示出了基于神经网络的逆运动学规划的示意性流程图。应注意，这只是为了帮助本领域技术人员更好地理解本发明实施例，而非限制本发明实施例的范围。如图3所示，对于具有冗余度的运动***，根据其已知的正运动学表达式得到对应的雅可比矩阵，同时考虑运动***的防止奇异、期望位姿、避障指标等多个期望指标，得到多目标逆运动规划描述，即动态优化模型，将动态优化模型代入神经网络模型，根据神经网络模型对应的状态方程进行求解，得到最优解关节速度
Figure PCTCN2016073367-appb-000050
以及关节自由度θ，将它们反馈给运动***，使得运动***按照最优的关节速度或关节自由度进行操作。
这里，本发明实施例采用神经网络对逆运动学规划问题进行在线优化，避免了复杂的参数化运输和推导过程，能够通过神经网络实时输出逆运动学规划问题的最优自由度速度信息。神经网络模型的建模过程可参见现有技术，这里不再赘述。
应理解，神经网络的状态方程，描述了神经网络的模型和学习规则，可以理解为一个功能模块，其物理实现方式可以是神经形态芯片、数字信号处理器(Digital Signal Processor，简称为“DSP”)、软件模拟等，本发明对此 不作限定。
因此，本发明实施例的控制运动***的方法，根据运动***的可操作性指标，确定该运动***的防止奇异约束条件，再根据该防止奇异约束条件以及其他多个性能指标确定动态优化模型，进一步地，通过神经网络在线求解出该运动***的运动参数，无需离线训练，能够避免运动***发生奇异状态，从而增强了运动***的容错性。
下面将以图1中的机械臂的运动***为例，描述本发明的控制运动***的方法的实施过程。
假设图1中的机械臂的7个关节自由度的初始状态为
Figure PCTCN2016073367-appb-000051
机械臂的末端操作器要在操作空间完成一个半径为20厘米的圆周操作，并且要躲避操作空间内的两个障碍物，即机械臂的任意部位距离任何一个障碍物都要求在5厘米之外。两个障碍物的空间位置坐标分别是(0,-0.2,1)和(-0.1,0.1,0.8)。并且，在运动过程中，约束机械臂的各个关节自由度的速度
Figure PCTCN2016073367-appb-000052
的绝对值都必须小于1rad/s。其中，上述半径为20厘米的圆周操作的运动参考轨迹如下式(3)所示：
Figure PCTCN2016073367-appb-000053
其中，上述x0、y0、z0为该机械臂在笛卡尔坐标系中的初始状态。在采用本发明的控制运动***的方法求解上述机械臂的各个关节自由度，具体实施如下：
1)根据机械臂的正运动学表达式r＝f(θ)，求导得到以速度信息
Figure PCTCN2016073367-appb-000054
描述的运动学表达式
Figure PCTCN2016073367-appb-000055
其中J(θ)为f(θ)的雅可比矩；
2)采用速度信息
Figure PCTCN2016073367-appb-000056
描述该机械臂在逆运动学规划中期望的多个指标：
能量指标用
Figure PCTCN2016073367-appb-000057
表示，关节速度指标用
Figure PCTCN2016073367-appb-000058
表示；轨迹追踪用
Figure PCTCN2016073367-appb-000059
表示，对于本例而言，对上式(3)求导，得到的轨迹追踪约束条件的具体形式如下所示：
Figure PCTCN2016073367-appb-000060
躲避障碍物的避障约束条件采用
Figure PCTCN2016073367-appb-000061
表示，这里，OC＝(OC1；OC2)，OC1是由第一个障碍物(0,-0.2,1)到机械臂的投影向量计算获得，OC2第二个障碍物(-0.1,0.1,0.8)到机械臂的投影向量计算获得，Jc(θ)的符号表达式与J(θ)相同；防止奇异约束条件采用
Figure PCTCN2016073367-appb-000062
表示，其中
Figure PCTCN2016073367-appb-000063
det表示矩阵行列式；
3)根据上述多个期望指标确定动态优化模型：
Figure PCTCN2016073367-appb-000064
其中，该
Figure PCTCN2016073367-appb-000065
为该θ的上限，该
Figure PCTCN2016073367-appb-000066
为该θ的下限θmin，这里
Figure PCTCN2016073367-appb-000067
为-1rad/s，
Figure PCTCN2016073367-appb-000068
为1rad/s。
4)将上述3)中的动态优化模型以及θ的初值代入神经网络模型的状态方程中，运行该神经网络，得到神经网络的输出，即该采样时刻机械臂的各个关节自由度的最优数值解。
上面1)到4)给出了本例中机械臂的基于神经网络的逆运动学规划方法，该方法可以通过仿真进行验证，例如，可以在VC6.0(即Microsoft Visual C++6.0)环境、Matlab环境下进行编程仿真实现逆运动学规划方法，对此不作限制。
下面将结合图4至图6描述本例中该机械臂的在线逆运动学规划的仿真结果。应注意，这只是为了帮助本领域技术人员更好地理解本发明实施例，而非限制本发明实施例的范围。
图4示出了机械臂的运动轨迹仿真结果图。如图4所示，机械臂运动路径的操作空间的三条轴分别为x轴(m)、y轴(m)、z轴(m)。在笛卡尔坐标系中，两个黑点分别对应障碍物的空间坐标(0,-0.2,1)和(-0.1,0.1,0.8)。仿真结果 表明，该机械臂可以很好的完成需要的半径为20厘米圆周操作，并且在运动过程中没有碰撞障碍物，也没有产生奇异状态。这里，产生奇异可以理解为两个杆重合为一条直线，即丧失一个自由度。
图5示出了机械臂的关节自由度的速度信息仿真结果图。如图5所示，横轴t为时间(s)，纵轴关节速度(rad/s)，图中7条线分别代表7个关节自由度的速度信息。仿真结果表明，在运动过程中，7个关节自由度的速度
Figure PCTCN2016073367-appb-000069
的绝对值在任意时刻均控制在1rad/s内。其中，有个关节不需要移动，即其输出值与x轴重合。
图6示出了机械臂的可操作性指数仿真结果图。如图6所示，横轴t为时间(s)，纵轴M表示可操作性指数，即为本发明实施例的防止约束奇异条件，图中仿真结果1为本发明的可操作性指数，仿真结果2为未采用本发明技术方案的可操作性指数。仿真结果表明，如果不采用本发明的技术方案，在第4s到第6s运动区间内，仿真结果2发生了奇异状态，可操作性指数的值趋于0，而采用本发明的技术方案，仿真结果1则没有出现奇异状态，从而体现出本发明的技术方案的优越性。
在本发明实施例中，机械臂根据多个性能指标确定动态优化模型，该性能指标包括能量最小、速度最小、轨迹跟踪、防止奇异和躲避障碍物，进一步地，通过神经网络在线求解该动态优化模型，得到该机械臂的7个关节自由度的最优数值解，无需离线训练，能够避免机械臂发生奇异状态，从而增强了***的容错性。
应理解，在本发明的各种实施例中，上述各过程的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本发明实施例的实施过程构成任何限定。
上文中详细描述了根据本发明实施例的控制运动***的方法，下面将描述根据本发明实施例的控制运动***的装置。
图7示出了根据本发明实施例的控制运动***的装置700的示意性框图。如图7所示，该装置700包括：
确定模块710，用于根据该运动***的可操作性指标，确定该运动***的防止奇异约束条件，该防止奇异约束条件约束该运动***的可操作性的值大于0；
优化模块720，用于根据该确定模块710确定的该防止奇异约束条件确 定该运动***的动态优化模型；
处理模块730，用于根据该优化模块720确定的该动态优化模型确定该运动***的运动参数；
控制模块740，用于根据该处理模块730确定的该运动参数控制该运动***。
本发明实施例的控制运动***的方法，根据运动***的可操作性指标，确定该运动***的防止奇异约束条件，再根据该防止奇异约束条件确定的动态优化模型在线求解出该运动***的运动参数，能够避免运动***发生奇异状态，从而增强了运动***的容错性。
在本发明实施例中，可选地，该确定模块710还用于根据该运动***的能量指标和速度指标确定目标函数；
其中，该优化模块720具体用于：
根据该确定模块710确定的该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
在本发明实施例中，可选地，该确定模块710还用于根据该运动***的运动参考轨迹，确定轨迹追踪约束条件；
该确定模块710还用于根据该运动***的避障安全距离，确定避障约束条件，该避障约束条件约束该运动***的运动方向在该运动***与该障碍物的距离趋于该避障安全距离时为远离该障碍物的方向；
其中，该优化模块720具体用于：
根据该轨迹追踪约束条件、该避障约束条件、该目标函数和该防止奇异约束条件，确定该运动***的该动态优化模型。
在本发明实施例中，可选地，该优化模块720具体用于：
根据下列公式确定该动态优化模型，
Figure PCTCN2016073367-appb-000070
其中，该运动***为n个关节自由度θ＝(θ1,θ2,...θn)的运动***，该
Figure PCTCN2016073367-appb-000071
为该θ对时间t求导的导数的二范数的平方，该||·||2表示二范数，该
Figure PCTCN2016073367-appb-000072
为该 θ对该t求导的导数的无穷范数的平方，该||·||∞表示无穷范数，该
Figure PCTCN2016073367-appb-000073
为该目标函数，该
Figure PCTCN2016073367-appb-000074
为该轨迹追踪约束条件，该
Figure PCTCN2016073367-appb-000075
为该运动***的正运动学表达式r＝f(θ)对该t求导的表达式，该J(θ)为该f(θ)的雅可比矩阵，该
Figure PCTCN2016073367-appb-000076
为该避障约束条件，该
Figure PCTCN2016073367-appb-000077
是由障碍物O指向运动关节C的向量，该Jc(θ)为所述运动关节C对应的雅可比矩阵，该
Figure PCTCN2016073367-appb-000078
为该防止奇异约束条件，该
Figure PCTCN2016073367-appb-000079
该δ为大于0的预定阈值，该
Figure PCTCN2016073367-appb-000080
该det表示矩阵行列式，该
Figure PCTCN2016073367-appb-000081
为该θ的上限θmax对该t求导的导数，该
Figure PCTCN2016073367-appb-000082
为该θ的下限θmin对该t求导的导数。
在本发明实施例中，可选地，该处理模块730具体用于：
根据该动态优化模型对应的神经网络模型，确定该运动***的该运动参数。
在本发明实施例中，可选地，该处理模块730具体用于：
根据以下该神经网模型的状态方程确定该运动参数，
Figure PCTCN2016073367-appb-000083
其中，该μ和该ρ均为该状态方程的状态参数，该ε为增益，该g为
Figure PCTCN2016073367-appb-000084
该J(θ)T为该J(θ)的转置矩阵，该A为
Figure PCTCN2016073367-appb-000085
该AT为该A的转置矩阵，该K为n×n矩阵，且该K矩阵的第k行第k列元素为1其余元素均为0，该b为
Figure PCTCN2016073367-appb-000086
因此，本发明实施例的控制运动***的装置，根据运动***的可操作性指标，确定所述运动***的防止奇异约束条件，再根据该防止奇异约束条件以及其他多个性能指标确定动态优化模型，进一步地，通过神经网络在线求解出该运动***的运动参数，无需离线训练，能够避免运动***发生奇异状 态，从而增强了运动***的容错性。
根据本发明实施例的控制运动***的装置700可执行根据本发明实施例的控制运动***的方法，并且该装置700中的各个模块的上述和其它操作和/或功能分别为了实现前述各个方法的相应流程，为了简洁，在此不再赘述。
图8示出了本发明的又一实施例提供的控制运动***的装置的结构，包括至少一个处理器802(例如CPU)，至少一个网络接口805或者其他通信接口，存储器806，和至少一个通信总线803，用于实现这些装置之间的连接通信。处理器802用于执行存储器806中存储的可执行模块，例如计算机程序。存储器806可能包含高速随机存取存储器(RAM：Random Access Memory)，也可能还包括非不稳定的存储器(non-volatile memory)，例如至少一个磁盘存储器。通过至少一个网络接口805(可以是有线或者无线)实现与至少一个其他网元之间的通信连接。
在一些实施方式中，存储器806存储了程序8061，处理器802执行程序8061，用于执行前述本发明实施例的控制运动***的方法。
应理解，本文中术语“和/或”，仅仅是一种描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。另外，本文中字符“/”，一般表示前后关联对象是一种“或”的关系。
应理解，在本发明的各种实施例中，上述各过程的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本发明实施例的实施过程构成任何限定。
本领域普通技术人员可以意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。
所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的***、装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。
在本申请所提供的几个实施例中，应该理解到，所揭露的***、装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示 意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个***，或一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外，在本发明各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。
所述功能如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以所述权利要求的保护范围为准。

Claims (13)

  1. 一种控制运动***的方法，其特征在于，包括：
    根据所述运动***的可操作性指标，确定所述运动***的防止奇异约束条件，所述防止奇异约束条件约束所述运动***的可操作性的值大于0；
    根据所述防止奇异约束条件确定所述运动***的动态优化模型；
    根据所述动态优化模型确定所述运动***的运动参数；
    根据所述运动参数控制所述运动***。
  2. 根据权利要求1所述的方法，其特征在于，所述方法还包括：
    根据所述运动***的能量指标和速度指标，确定目标函数；
    其中，所述根据所述防止奇异约束条件确定所述运动***的动态优化模型，包括：
    根据所述目标函数和所述防止奇异约束条件，确定所述运动***的所述动态优化模型。
  3. 根据权利要求2所述的方法，其特征在于，所述方法还包括：
    根据所述运动***的运动参考轨迹，确定轨迹追踪约束条件；
    根据所述运动***的避障安全距离，确定避障约束条件，所述避障约束条件约束所述运动***的运动方向在所述运动***与所述障碍物的距离趋于所述避障安全距离时为远离所述障碍物的方向；
    其中，所述根据所述防止奇异约束条件确定所述运动***的动态优化模型，包括：
    根据所述轨迹追踪约束条件、所述避障约束条件、所述目标函数和所述防止奇异约束条件，确定所述运动***的所述动态优化模型。
  4. 根据权利要求3所述的方法，其特征在于，所述根据所述轨迹追踪约束条件、所述避障约束条件、所述目标函数和所述防止奇异约束条件，确定所述运动***的所述动态优化模型，包括：
    根据下列公式确定所述动态优化模型，
    Figure PCTCN2016073367-appb-100001
    Figure PCTCN2016073367-appb-100002
    Figure PCTCN2016073367-appb-100003
    Figure PCTCN2016073367-appb-100004
    Figure PCTCN2016073367-appb-100005
    其中，所述运动***为n个关节自由度θ＝(θ1,θ2,...θn)的运动***，所述
    Figure PCTCN2016073367-appb-100006
    为所述θ对时间t求导的导数的二范数的平方，所述||·||2表示二范数，所述
    Figure PCTCN2016073367-appb-100007
    为所述θ对所述t求导的导数的无穷范数的平方，所述||·||∞表示无穷范数，所述
    Figure PCTCN2016073367-appb-100008
    为所述目标函数，所述
    Figure PCTCN2016073367-appb-100009
    为所述轨迹追踪约束条件，所述
    Figure PCTCN2016073367-appb-100010
    为所述运动***的正运动学表达式r＝f(θ)对所述t求导的表达式，所述J(θ)为所述f(θ)的雅可比矩阵，所述
    Figure PCTCN2016073367-appb-100011
    为所述避障约束条件，所述
    Figure PCTCN2016073367-appb-100012
    是由障碍物O指向运动关节C的向量，所述Jc(θ)为所述运动关节C对应的雅可比矩阵，所述
    Figure PCTCN2016073367-appb-100013
    为所述防止奇异约束条件，所述
    Figure PCTCN2016073367-appb-100014
    所述δ为大于0的预定阈值，所述
    Figure PCTCN2016073367-appb-100015
    所述det表示矩阵行列式，所述
    Figure PCTCN2016073367-appb-100016
    为所述θ的上限θmax对所述t求导的导数，所述
    Figure PCTCN2016073367-appb-100017
    为所述θ的下限θmin对所述t求导的导数。
  5. 根据权利要求4所述的方法，其特征在于，所述根据所述动态优化模型，确定所述运动***的所述运动参数包括：
    根据所述动态优化模型对应的神经网络模型，确定所述运动***的所述运动参数。
  6. 根据权利要求5所述的方法，其特征在于，所述根据所述动态优化模型对应的神经网络模型，确定所述运动***的所述运动参数，包括：
    根据以下所述神经网模型的状态方程确定所述运动参数，
    Figure PCTCN2016073367-appb-100018
    其中，所述μ和所述ρ均为所述状态方程的状态参数，所述ε为增益，所述g为
    Figure PCTCN2016073367-appb-100019
    所述J(θ)T为所述J(θ)的转置矩阵，所述A为
    Figure PCTCN2016073367-appb-100020
    所述AT为所述A的转置矩阵，所述K为n×n矩阵，且所述K矩阵的第k行第k列元素为1其余元素均为0，所述b为
    Figure PCTCN2016073367-appb-100021
  7. 一种控制运动***的装置，其特征在于，包括：
    确定模块，用于根据所述运动***的可操作性指标，确定所述运动***的防止奇异约束条件，所述防止奇异约束条件约束所述运动***的可操作性的值大于0；
    优化模块，用于根据所述确定模块确定的所述防止奇异约束条件确定所述运动***的动态优化模型；
    处理模块，用于根据所述优化模块确定的所述动态优化模型确定所述运动***的运动参数；
    控制模块，用于根据所述运动参数控制所述运动***。
  8. 根据权利要求7所述的装置，其特征在于，所述确定模块还用于根据所述运动***的能量指标和速度指标确定目标函数；
    其中，所述优化模块具体用于：
    根据所述确定模块确定的所述目标函数和所述防止奇异约束条件，确定所述运动***的所述动态优化模型。
  9. 根据权利要求8所述的装置，其特征在于，所述确定模块还用于根据所述运动***的运动参考轨迹，确定轨迹追踪约束条件；
    所述确定模块还用于根据所述运动***的避障安全距离，确定避障约束条件，所述避障约束条件约束所述运动***的运动方向在所述运动***与所述障碍物的距离趋于所述避障安全距离时为远离所述障碍物的方向；
    其中，所述优化模块具体用于：
    根据所述轨迹追踪约束条件、所述避障约束条件、所述目标函数和所述防止奇异约束条件，确定所述运动***的所述动态优化模型。
  10. 根据权利要求9所述的装置，其特征在于，所述优化模块具体用于：
    根据下列公式确定所述动态优化模型，
    Figure PCTCN2016073367-appb-100022
    Figure PCTCN2016073367-appb-100023
    Figure PCTCN2016073367-appb-100024
    Figure PCTCN2016073367-appb-100025
    Figure PCTCN2016073367-appb-100026
    其中，所述运动***为n个关节自由度θ＝(θ1,θ2,...θn)的运动***，所述
    Figure PCTCN2016073367-appb-100027
    为所述θ对时间t求导的导数的二范数的平方，所述||·||2表示二范数，所述
    Figure PCTCN2016073367-appb-100028
    为所述θ对所述t求导的导数的无穷范数的平方，所述||·||∞表示无穷范数，所述
    Figure PCTCN2016073367-appb-100029
    为所述目标函数，所述
    Figure PCTCN2016073367-appb-100030
    为所述轨迹追踪约束条件，所述
    Figure PCTCN2016073367-appb-100031
    为所述运动***的正运动学表达式r＝f(θ)对所述t求导的表达式，所述J(θ)为所述f(θ)的雅可比矩阵，所述
    Figure PCTCN2016073367-appb-100032
    为所述避障约束条件，所述
    Figure PCTCN2016073367-appb-100033
    是由障碍物O指向运动关节C的向量，所述
    Figure PCTCN2016073367-appb-100034
    为所述防止奇异约束条件，所述
    Figure PCTCN2016073367-appb-100035
    所述δ为大于0的预定阈值，所述
    Figure PCTCN2016073367-appb-100036
    所述det表示矩阵行列式，所述
    Figure PCTCN2016073367-appb-100037
    为所述θ的上限θmax对所述t求导的导数，所述
    Figure PCTCN2016073367-appb-100038
    为所述θ的下限θmin对所述t求导的导数。
  11. 根据权利要求10所述的装置，其特征在于，所述处理模块具体用于：
    根据所述动态优化模型对应的神经网络模型，确定所述运动***的所述运动参数。
  12. 根据权利要求11所述的装置，其特征在于，所述处理模块具体用于：
    根据以下所述神经网模型的状态方程确定所述运动参数，
    Figure PCTCN2016073367-appb-100039
    其中，所述μ和所述ρ均为所述状态方程的状态参数，所述ε为增益，所述g为
    Figure PCTCN2016073367-appb-100040
    所述J(θ)T为所述J(θ)的转置矩阵，所述A为
    Figure PCTCN2016073367-appb-100041
    所述AT为所述A的转置矩阵，所述K为n×n矩阵，且所述K矩阵的第k行第k列元素为1其余元素均为0，所述b为
    Figure PCTCN2016073367-appb-100042
  13. 一种控制运动***的装置，其特征在于，包括：处理器、存储器和通 信接口；
    所述处理器与所述存储器和所述通信接口连接，所述存储器用于存储指令，所述处理器用于执行所述指令，所述通信接口用于在所述处理器的控制下与其他网元进行通信，当所述装置运行时，所述处理器执行所述存储器存储的所述指令，以使所述装置执行所述权利要求1至6中任一项所述的方法。
PCT/CN2016/073367 2016-02-03 2016-02-03 控制运动***的方法和装置 WO2017132905A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PCT/CN2016/073367 WO2017132905A1 (zh) 2016-02-03 2016-02-03 控制运动***的方法和装置

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/CN2016/073367 WO2017132905A1 (zh) 2016-02-03 2016-02-03 控制运动***的方法和装置

Publications (1)

Publication Number Publication Date
WO2017132905A1 true WO2017132905A1 (zh) 2017-08-10

Family

ID=59500377

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2016/073367 WO2017132905A1 (zh) 2016-02-03 2016-02-03 控制运动***的方法和装置

Country Status (1)

Country Link
WO (1) WO2017132905A1 (zh)

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108422424A (zh) * 2018-05-28 2018-08-21 兰州大学 一种具有饱和特性的抗扰动机械臂重复运动规划方法
CN110795856A (zh) * 2019-11-04 2020-02-14 首都师范大学 机械臂稳定性形式化分析方法、装置、设备及存储介质
CN112346419A (zh) * 2020-10-30 2021-02-09 深圳市烨嘉为技术有限公司 人机安全交互方法、机器人及计算机可读存储介质
CN112914601A (zh) * 2021-01-19 2021-06-08 深圳市德力凯医疗设备股份有限公司 一种机械臂的避障方法、装置、存储介质及超声设备
CN114378827A (zh) * 2022-01-26 2022-04-22 北京航空航天大学 一种基于移动机械臂整体控制的动态目标跟踪抓取方法
CN114536348A (zh) * 2022-04-08 2022-05-27 北京邮电大学 一种高欠驱动空间机械臂运动灵巧性评估方法
CN115609595A (zh) * 2022-12-16 2023-01-17 北京中海兴达建设有限公司 一种机械臂的轨迹规划方法、装置、设备及可读存储介质
CN115847404A (zh) * 2022-11-28 2023-03-28 燕山大学 一种基于复合学习的受限机械臂有限时间控制方法

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080065359A1 (en) * 2006-07-15 2008-03-13 Rudolph Lee N Methods and Apparati for Efficiently Parametrizing, Describing, Generating, Modifying and Manipulating Configurations, Conformations, and Deformations of Systems That Comprise Multiple Physical or Virtual Objects
CN101804627A (zh) * 2010-04-02 2010-08-18 中山大学 一种冗余度机械臂运动规划方法
US20100332030A1 (en) * 2009-06-24 2010-12-30 Intuitive Surgical, Inc. Arm with a combined shape and force sensor
CN102495550A (zh) * 2011-11-21 2012-06-13 湖南湖大艾盛汽车技术开发有限公司 并联机器人的正、逆动力学响应分析与控制方法
CN103077310A (zh) * 2013-01-04 2013-05-01 同济大学 基于螺旋空间夹角的串联和并联机器人机构的奇异裕度检测方法
CN103213129A (zh) * 2013-04-17 2013-07-24 北京空间飞行器总体设计部 一种空间机械臂位置力混合控制方法
CN103955619A (zh) * 2014-05-09 2014-07-30 大连大学 一种七自由度空间机械臂最小基座扰动解析逆运动学求解方法
CN104723340A (zh) * 2015-03-07 2015-06-24 哈尔滨工业大学 基于连接和阻尼配置的柔性关节机械臂的阻抗控制方法
CN104772773A (zh) * 2015-05-08 2015-07-15 首都师范大学 一种机械臂运动学形式化分析方法
CN104809276A (zh) * 2015-04-14 2015-07-29 长安大学 一种多手指机器人动力学解析模型及其建模方法
CN104842355A (zh) * 2015-01-20 2015-08-19 西北工业大学 避障约束下冗余空间机器人的混合整数预测控制方法

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20080065359A1 (en) * 2006-07-15 2008-03-13 Rudolph Lee N Methods and Apparati for Efficiently Parametrizing, Describing, Generating, Modifying and Manipulating Configurations, Conformations, and Deformations of Systems That Comprise Multiple Physical or Virtual Objects
US20100332030A1 (en) * 2009-06-24 2010-12-30 Intuitive Surgical, Inc. Arm with a combined shape and force sensor
CN101804627A (zh) * 2010-04-02 2010-08-18 中山大学 一种冗余度机械臂运动规划方法
CN102495550A (zh) * 2011-11-21 2012-06-13 湖南湖大艾盛汽车技术开发有限公司 并联机器人的正、逆动力学响应分析与控制方法
CN103077310A (zh) * 2013-01-04 2013-05-01 同济大学 基于螺旋空间夹角的串联和并联机器人机构的奇异裕度检测方法
CN103213129A (zh) * 2013-04-17 2013-07-24 北京空间飞行器总体设计部 一种空间机械臂位置力混合控制方法
CN103955619A (zh) * 2014-05-09 2014-07-30 大连大学 一种七自由度空间机械臂最小基座扰动解析逆运动学求解方法
CN104842355A (zh) * 2015-01-20 2015-08-19 西北工业大学 避障约束下冗余空间机器人的混合整数预测控制方法
CN104723340A (zh) * 2015-03-07 2015-06-24 哈尔滨工业大学 基于连接和阻尼配置的柔性关节机械臂的阻抗控制方法
CN104809276A (zh) * 2015-04-14 2015-07-29 长安大学 一种多手指机器人动力学解析模型及其建模方法
CN104772773A (zh) * 2015-05-08 2015-07-15 首都师范大学 一种机械臂运动学形式化分析方法

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
CAO, XIAOTAO ET AL.: "Robust RBF neural network force/position control of time varying constrained flexible manipulator", CONTROL AND DECISION, vol. 22, 30 September 2007 (2007-09-30), pages 977 - 982 and 988, ISSN: 1001-0920 *
FANG, BIN ET AL.: "Position resolution and singularity analysis of the I4R parallel manipulator mechanism", CHINESE HIGH TECHNOLOGY LETTERS, vol. 20, no. 10, 31 October 2010 (2010-10-31), pages 1080 - 1085, ISSN: 1002-0470 *
FU, YILI ET AL.: "Research on Kinematic Characteristic of Free Floating Space Robot with Zero-disturbance Spacecraft Attitude", JOURNAL OF ASTRONAUTICS, vol. 29, 30 November 2008 (2008-11-30) *
KE , WENDE ET AL.: "A Study of Walking Movement Control of Humanoid Robot", JOURNAL OF MAOMING COLLEGE, vol. 22, no. 4, 31 August 2012 (2012-08-31), pages 30 - 33 *

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108422424A (zh) * 2018-05-28 2018-08-21 兰州大学 一种具有饱和特性的抗扰动机械臂重复运动规划方法
CN110795856B (zh) * 2019-11-04 2023-04-14 首都师范大学 机械臂稳定性形式化分析方法、装置、设备及存储介质
CN110795856A (zh) * 2019-11-04 2020-02-14 首都师范大学 机械臂稳定性形式化分析方法、装置、设备及存储介质
CN112346419A (zh) * 2020-10-30 2021-02-09 深圳市烨嘉为技术有限公司 人机安全交互方法、机器人及计算机可读存储介质
CN112346419B (zh) * 2020-10-30 2021-12-31 深圳市烨嘉为技术有限公司 人机安全交互方法、机器人及计算机可读存储介质
CN112914601A (zh) * 2021-01-19 2021-06-08 深圳市德力凯医疗设备股份有限公司 一种机械臂的避障方法、装置、存储介质及超声设备
CN112914601B (zh) * 2021-01-19 2024-04-02 深圳市德力凯医疗设备股份有限公司 一种机械臂的避障方法、装置、存储介质及超声设备
CN114378827A (zh) * 2022-01-26 2022-04-22 北京航空航天大学 一种基于移动机械臂整体控制的动态目标跟踪抓取方法
CN114378827B (zh) * 2022-01-26 2023-08-25 北京航空航天大学 一种基于移动机械臂整体控制的动态目标跟踪抓取方法
CN114536348A (zh) * 2022-04-08 2022-05-27 北京邮电大学 一种高欠驱动空间机械臂运动灵巧性评估方法
CN114536348B (zh) * 2022-04-08 2023-05-26 北京邮电大学 一种高欠驱动空间机械臂运动灵巧性评估方法
CN115847404A (zh) * 2022-11-28 2023-03-28 燕山大学 一种基于复合学习的受限机械臂有限时间控制方法
CN115609595A (zh) * 2022-12-16 2023-01-17 北京中海兴达建设有限公司 一种机械臂的轨迹规划方法、装置、设备及可读存储介质

Similar Documents

Publication Publication Date Title
WO2017132905A1 (zh) 控制运动***的方法和装置
Kong et al. Adaptive fuzzy control for coordinated multiple robots with constraint using impedance learning
US11845186B2 (en) Inverse kinematics solving method for redundant robot and redundant robot and computer readable storage medium using the same
WO2018107851A1 (zh) 冗余机械臂的控制方法及装置
Yang et al. Neural-learning-based telerobot control with guaranteed performance
CN107490965B (zh) 一种空间自由漂浮机械臂的多约束轨迹规划方法
Lu et al. Collision-free and smooth joint motion planning for six-axis industrial robots by redundancy optimization
Zhang et al. Variable joint-velocity limits of redundant robot manipulators handled by quadratic programming
CN107877517B (zh) 基于CyberForce遥操作机械臂的运动映射方法
Luo et al. Real time human motion imitation of anthropomorphic dual arm robot based on Cartesian impedance control
Shi et al. Collision avoidance for redundant robots in position-based visual servoing
Mukherjee et al. Inverse kinematics of a NAO humanoid robot using kinect to track and imitate human motion
Zhang et al. Two hybrid multiobjective motion planning schemes synthesized by recurrent neural networks for wheeled mobile robot manipulators
CN114571469A (zh) 一种机械臂零空间实时避障控制方法及***
Kim et al. Modified configuration control with potential field for inverse kinematic solution of redundant manipulator
Elsayed et al. Mobile manipulation using a snake robot in a helical gait
Yan et al. Analytical inverse kinematics of a class of redundant manipulator based on dual arm-angle parameterization
Teke et al. Real-time and robust collaborative robot motion control with Microsoft Kinect® v2
CN114378809A (zh) 软体机器人操纵器的无奇点运动学参数化
Wang et al. Automatic obstacle avoidance using redundancy for shared controlled telerobot manipulator
Sadeghian et al. Visual servoing with safe interaction using image moments
Wang et al. An online motion planning algorithm for a 7DOF redundant manipulator
Lin et al. Intuitive kinematic control of a robot arm via human motion
Ostanin et al. Programming by Demonstration Using Two-Step Optimization for Industrial Robot.
Gienger et al. Exploiting task intervals for whole body robot control

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 16888730

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 16888730

Country of ref document: EP

Kind code of ref document: A1