CN117075525B - Mobile robot control method based on constraint model predictive control - Google Patents
Mobile robot control method based on constraint model predictive control Download PDFInfo
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Abstract
The invention relates to a mobile robot control method based on constraint model predictive control, which comprises the following steps: performing kinematic modeling on a mobile robot comprising a mobile base and a mechanical arm; determining a real-time state of the mobile robot; based on a kinematic model and a real-time state of the robot, predicting future system states and behaviors by using model prediction control, solving a control problem by minimizing an objective function and meeting constraint conditions to obtain optimal control input in a future control time domain, and controlling the motion of the mobile robot in real time; and (5) iterating until the expected motion of the mobile robot is achieved. Wherein the constraints of the model predictive control include kinetic constraints on the robotic arm and/or the mobile base. The method can improve corresponding kinematic constraint based on the kinematic performances of the mobile base and the mechanical arm of the mobile robot, so that the control stability of the mobile robot is improved.
Description
Technical Field
The invention belongs to the technical field of robot motion control, and particularly relates to a mobile robot control method based on constrained model predictive control.
Background
Mobile robots are an automated device that can be flexibly operated in the fields of industry, medical treatment, service, etc. Mobile robots are generally composed of a mobile base and a robot arm mounted on the mobile base. In simple work tasks, motion bases are often used to achieve translational motion, they have two-dimensional planar motion degrees of freedom, while robotic arms are often composed of multiple joints, thus having multiple degrees of freedom motion, allowing complex pose and positional adjustments in three dimensions. However, in complex work tasks, cooperative movements of the mobile base and the robotic arm are often required to ensure that the movements therebetween are synchronized and smooth, which is critical to achieving efficient operation. Efficient coordination and control of the motion of the mobile base and the robotic arm is a complex task that requires consideration of the interaction between the two, as well as avoiding collisions and unnecessary motion when planning the path. Meanwhile, the control system needs to be capable of responding to environmental changes and task demands in real time, and the cooperation stability and high efficiency of the mechanical arm and the movable base are ensured.
However, compared with the traditional fixed mechanical arm, the mobile robot has high redundancy and weak structure, so that the problems of low cooperative efficiency, slow real-time response, obvious vibration phenomenon and the like exist in the operation process, and the stability of the whole system is reduced while the working efficiency and the operation precision are influenced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a mobile robot control method based on constrained model predictive control. The method can improve corresponding kinematic constraint based on the kinematic performances of the mobile base and the mechanical arm of the mobile robot, thereby improving the control stability of the mobile robot.
The invention provides a mobile robot control method based on constraint model predictive control, which comprises the following specific steps:
modeling a system: performing kinematic modeling on a mobile robot comprising a mobile base and a mechanical arm;
state estimation: determining a real-time state of the mobile robot;
model predictive control: based on a kinematic model and a real-time state of the robot, predicting future system states and behaviors by using model prediction control, solving a control problem by minimizing an objective function and meeting constraint conditions to obtain optimal control input in a future control time domain, and controlling the motion of the mobile robot in real time;
and (3) loop iteration: performing loop iteration in a new control period, re-determining the system state, performing model prediction, solving the optimal control input, and updating the control instruction in real time until the expected motion of the mobile robot is realized;
wherein the constraint conditions of model predictive control include dynamic constraints on the robotic arm and/or the mobile base; the kinetic constraints of the mobile base are:
v b ≤v b max ；
；
wherein v is b To move the baseTranslation speed v of (v) b max Maximum translation speed for the mobile base; phi (phi) b For the weight coefficient, d is the horizontal distance from the end effector to the task target, d b Threshold, v, for horizontal distance of end effector to task target low A lower speed limit for moving the base; v high A high speed limit for moving the base;
the kinetic constraints of the mechanical arm are:
ω k ≦ω k max ；
where k is the number of the selected joint of the mechanical arm, ω k Angular velocity, ω, of the kth joint of the mechanical arm k max Is the maximum angular velocity of the kth joint of the mechanical arm lambda k Is the weight coefficient omega of the kth joint of the mechanical arm k low The angular velocity of the kth joint of the mechanical arm is the lower limit; omega k high An angular velocity upper limit for the kth joint; p is the distance from the end effector to the task target, p max Is a threshold value for the distance of the end effector to the task target.
According to an aspect of the invention, d b Proportional to the size of the operating space of the mechanical arm.
According to an aspect of the invention, v low Is 0.
According to one aspect of the invention, p max Proportional to the size of the operating space of the mechanical arm.
Omega according to an aspect of the invention k low Is 0.
According to an aspect of the invention, the constraint further comprises:
x i+1 =f(x i ,u i )，x i the system state at the moment i;
x i e, X, i=0, … …, N-1, X is the system state constraint set;
u i e U, i=0, … …, N-1, U is the system input aboutA bundle set.
According to an aspect of the invention, the objective function of the model predictive control is:
wherein g is the position and pose deviation of the end effector, g=q des -q cur Q represents the position and the pose of the end effector, q des For the target position pose of the end effector, q cur For the real-time position and pose of the end effector, P, Q, R is a positive weighting matrix, N is a control time domain, u i Is the system input at time i in the future.
The invention also provides a computer readable storage medium having stored thereon a computer program for execution by a processor of any of the steps of the methods described in the foregoing.
The beneficial technical effects of the invention are as follows: the method can improve corresponding kinematic constraint based on the kinematic performances of the mobile base and the mechanical arm of the mobile robot, thereby improving the control stability of the mobile robot. Specifically, besides the system state constraint and the control input constraint, the method of the invention also sets dynamic constraint, namely, limits on actual movement according to the dynamic performances of the mechanical arm and the movable base, so that the control system is helped to keep stable, the performance of the control system is optimized, the control system is better adapted to actual application requirements, the control precision and efficiency are improved, and damage or collision of the mechanical arm or the movable base is avoided.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic view of a mobile robot according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of the kinematic constraints of a mobile base of a mobile robot according to an embodiment of the present invention;
fig. 3 is a schematic view of the dynamic constraints of the mechanical arm of the mobile robot according to an embodiment of the present invention.
Description of the embodiments
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
As shown in fig. 1, the specific structure of the mobile robot in the present invention generally includes the following main components:
and the moving base is positioned at the bottom of the robot and is used for providing stable support and space movement carrier for the robot. Common types of mobile bases include wheel types (e.g., four-wheel, two-wheel, three-wheel, omni-directional, etc.), foot types, track types, hybrid types (e.g., wheel, foot hybrid), special types (e.g., adsorption type, track type, snake type, etc.). Among them, the wheel-type and foot-type mobile base is the most frequently used mobile base. Wheel-type mobile bases use wheels as their primary means of movement, typically comprising two or more wheels, either fixed or rotating. The fixed wheels provide stable support, the rotating wheels are used for realizing the steering and motion control of the robot, and the driving mode of the wheel type movable base can be front wheel driving, rear wheel driving or all-wheel driving. Foot-type mobile bases employ animal-like leg structures, typically comprising a plurality of leg units. Each leg unit can be composed of a plurality of joints and actuators, so that the robot can walk, crawl or jump on different terrains, the driving mode of the foot-type moving base is controlled by the joints and actuators of each leg unit, and gait movement is achieved by adjusting the angles of the joints. The structure and driving manner of the moving base may vary depending on the manufacturer and the model of the robot. When the mobile robot is selected, the most suitable type of mobile base can be selected by comprehensively considering the functional requirements, the use environment, the budget and other factors of the mobile robot.
A mechanical arm; the most commonly used robotic arms are articulated robotic arms, which are typically connected by a plurality of joints and links. Each joint allows movement of the robotic arm in a different direction, the types of joints including: a rotary joint that allows the mechanical arm to perform a rotary motion in one plane; and a sliding joint allowing the mechanical arm to perform sliding movement along a straight line direction. The combination and number of these joints determines the degrees of freedom of the robotic arm, i.e. the different modes of motion and poses that can be achieved. The joints are connected by connecting rods to form a framework of the mechanical arm. The length and shape of the links can be designed according to the application requirements.
An end effector; the end of the robotic arm is typically equipped with one or more actuators for performing specific tasks. The end effector may be a jaw, chuck, laser head, welding gun, etc., depending on the application.
A driver; the moving base and the mechanical arm are moved by a driver. Common drives include motors, hydraulic systems, pneumatic systems, and the like. Motors are the most common type of drive that can be precisely controlled by helical gears, speed reducers, encoders, and the like.
A control system for managing and controlling the mobile robot movements and performing tasks. The control system is typically composed of a computer, sensors, etc. for monitoring and adjusting the movements of the mobile robot in real time.
The structure and the movement mode of the movable base and the mechanical arm are different, so that the difference exists in the kinematic characteristics. The mobile base is typically a platform whose kinematic characteristics relate primarily to position and attitude. In a planar motion base, there are typically three degrees of freedom, including translation in the x and y directions and rotation about the z-axis. In a three-dimensional motion base, there are additional degrees of freedom, such as rotation about the x and y axes. The kinematic characteristics of the robotic arm relate to the angle of the plurality of joints and the position and attitude of the end effector. The specific number of degrees of freedom depends on the configuration of the robotic arm, and typically ranges from 3 degrees of freedom to 6 degrees of freedom.
The difference in kinematic characteristics determines the difference in kinematic control for the motion base and the robotic arm. The kinematic control method of the mobile base mainly relates to position control and attitude control. The position control enables the robot to realize translational and rotational movement by controlling driving devices such as wheels, feet or tracks of the base. Attitude control involves controlling the attitude angle of the base so that the robot maintains a desired orientation. The kinematics control method of the mechanical arm mainly relates to joint angle and position and posture control of the end effector. Joint angle control rotates each joint of the mechanical arm to a desired angle by driving a motor or hydraulic system of each joint. The position and posture of the end effector are controlled by calculating the relation between the joint angle and the posture of the end effector through a forward kinematics model, so that the end effector is accurately controlled.
It should be noted that the mobile base and the robotic arm are typically combined to form a complete mobile robotic system. In the mobile robot control method, the kinematic characteristics of the mobile base and the mechanical arm are considered at the same time, and the mobile base and the mechanical arm move in a coordinated manner so as to realize the expected task of the robot.
The invention provides a mobile robot control method based on model predictive control, which can predict future states in the motion process of a mobile robot and take corresponding control actions to optimize the motion and performance of the robot. Wherein the constraints of the model predictive control include kinetic constraints on the robotic arm and/or the mobile base. The method can improve corresponding kinematic constraint based on the kinematic performances of the mobile base and the mechanical arm of the mobile robot, so that the control stability of the mobile robot is improved. The following description will be made with reference to a mobile robot in which the mobile base is a four-wheel mobile base and the robot arm is a six-degree-of-freedom robot.
Example 1
An embodiment provides a mobile robot control method based on constraint predictive control, which specifically includes the following steps:
modeling a system: first, a mobile robot is kinematically modeled, including the structure, dynamics, kinematics, etc. of the mobile base and the robotic arm. The corresponding mathematical model can be obtained by adopting a machine learning method, a system identification technology or physical modeling and other means.
State estimation: a real-time status of the mobile robot is determined. In actual operation, it is necessary to estimate the state of the robot in real time, including the positions, attitudes, speeds, etc. of the moving base and the robot arm. This may be achieved by sensor data fusion and filtering techniques such as Extended Kalman Filtering (EKF) or Particle Filtering (PF), etc.
Model predictive control: based on the kinematic model and the real-time state of the robot, the model predictive control is used for predicting the future system state and behavior, and the control problem is solved by minimizing the objective function and meeting the constraint condition, so that the optimal control input in the future control time domain is obtained, and the motion of the mobile robot is controlled in real time.
And (3) loop iteration: and (3) carrying out loop iteration in a new control period, re-determining the system state, carrying out model prediction, solving the optimization problem, and updating the control instruction in real time until the expected motion of the mobile robot is realized. The model prediction control is an iterative optimization process, and loop iteration needs to be carried out in each control period, so that the state is estimated again in each period, model prediction is carried out, the optimization problem is solved, and the control instruction is updated in real time until the expected motion of the mobile robot is realized.
The objective function of the model predictive control is as follows:
wherein g is the position and pose deviation of the end effector, g=q des -q cur ，qRepresenting the position and pose of the end effector, i.e. [ q ] x ,q y ,q z ,r x ,r y ,r z ] T ,q des For the target position pose of the end effector, q cur For the real-time position and pose of the end effector, P, Q, R is a positive weighting matrix, N is a control time domain, u i For system input at time i in the future, i.e. [ v ] b,x ,v b,y ,ω b ,ω 1 ,ω 2 ,ω 3 ,ω 4 ,ω 5 ,ω 6 ] T ，(v b,x ,v b,y ) Representing the speed, ω, of movement of the moving base along the x-axis and the y-axis, respectively b Representing the angular velocity of rotation of the mobile base, i.e. the angular velocity of rotation of the mobile base about its vertical axis, (ω) 1 ,ω 2 ,ω 3 ,ω 4 ,ω 5 ,ω 6 ) Is the angular velocity of each joint of the mechanical arm. Parameters in the objective function can be optimized through experiments and debugging, so that the optimal control performance is obtained.
The objective function of model predictive control is very critical, it directly affects the performance and effectiveness of the control method, and it is necessary to select appropriate metrics and trade-offs according to specific control tasks and system requirements.
Constraints of model predictive control refer to constraints imposed on system states, control inputs, or other related variables. These constraints are set to ensure that the control system meets the requirements of the actual application and system performance during operation. Constraints in this embodiment include system state constraints, control input constraints, and dynamics constraints. The system state constraint is a limitation set on state variables such as the position, the posture, the speed and the like of the mechanical arm or the moving base, for example, the joint angle of the mechanical arm should be kept within a safe range, the positions of the moving base and the mechanical arm should be limited in a working area and the like; control input constraints, which are limitations set on the actuator output or control commands of the robotic arm and motion base, for example, the magnitude of the control input should be limited within the rated range of the motor to avoid damaging the motor or equipment. The system state constraints and the control input constraints include:
x i+1 =f(x i ,u i ) I.e. x i+1 Is x i And u i Functions of (2), e.g. x i+1 =Ax i +Bu i ，x i The system state at the moment i;
x i e, X, i=0, … …, N-1, X is the system state constraint set;
u i e U, i=0, … …, N-1, U is the system input constraint set.
Besides the system state constraint and the control input constraint, the embodiment also sets dynamic constraint, namely, limits on actual movement of the mechanical arm and the movable base according to dynamic performance of the mechanical arm and the movable base, so that the control system is helped to keep stable, performance of the control system is optimized, the control system is better adapted to actual application requirements, control precision and efficiency are improved, and damage or collision of the mechanical arm or the movable base is avoided.
The movable base is generally heavy in weight and slow in dynamic response, and the mechanical arm is light in weight, fast in dynamic response and higher in control precision, so that great difference exists between the dynamic performance of the movable base and the dynamic response. As shown in fig. 2 and 3, the dynamic constraint conditions of the moving base and the mechanical arm are redesigned in this embodiment, wherein the dynamic constraint conditions of the moving base are as follows:
v b ≤v b max ，v b to move the translation speed of the base, v b max Maximum translation speed for the mobile base;
the method comprises the steps of carrying out a first treatment on the surface of the Wherein phi is b For the weight coefficient, d is the horizontal distance from the end effector to the task target, d b A threshold value for the horizontal distance of the end effector to the task target, which is proportional to the size of the operating space of the manipulator, v low The value of the speed lower limit of the movable base can be 0; v high Is the high speed limit for moving the base.
The kinetic constraints of the mechanical arm are:
ω k ≦ω k max ，ω k is a mechanical armAngular velocity, ω, of the kth joint k max Maximum angular velocity for the kth joint;
the method comprises the steps of carrying out a first treatment on the surface of the Wherein k is a natural number between 1 and 6, i.e. one (kth) or some joints of the mechanical arm can be selected for dynamic constraint, lambda k As the weight coefficient omega k low The value of the angular velocity lower limit of the kth joint is 0; omega k high An angular velocity upper limit for the kth joint; p is the distance from the end effector to the task target, p max The threshold value, which is the distance of the end effector to the task target, is proportional to the size of the operating space of the robotic arm.
The dynamic constraints on the motion base and the robotic arm may be used separately or in combination in different embodiments or applications, respectively. When the mechanical arm is far away from the target, the maximum speed value of the moving base is large, so that rapid translational movement is realized, and meanwhile, the maximum speed of the mechanical arm is low (the value can be 0), so that the mechanical arm is kept still; as the robot approaches the task target quickly, and the task target is in the optimal working interval of the mechanical arm, the maximum speed of the movable base is reduced, so that the movable base is kept stable, and meanwhile, the maximum speed of the mechanical arm is increased quickly, so that the operation is started; when the end effector of the robotic arm is less than the collision threshold from the target, the maximum speed of the robotic arm should be rapidly reduced to prevent collisions.
(second) embodiment II
An embodiment II provides a mobile robot method based on model predictive control. The method comprises the following specific steps:
modeling a system: first, a mobile robot is kinematically modeled, including the structure, dynamics, kinematics, etc. of the mobile base and the robotic arm. The corresponding mathematical model can be obtained by adopting a machine learning method, a system identification technology or physical modeling and other means.
State estimation: a real-time status of the mobile robot is determined. In actual operation, it is necessary to estimate the state of the robot in real time, including the positions, attitudes, speeds, etc. of the moving base and the robot arm. This may be achieved by sensor data fusion and filtering techniques such as Extended Kalman Filtering (EKF) or Particle Filtering (PF), etc.
Model predictive control: based on the kinematic model and the real-time state of the robot, the model predictive control is used for predicting the future system state and behavior, and the control problem is solved by minimizing the objective function and meeting the constraint condition, so that the optimal control input in the future control time domain is obtained, and the motion of the mobile robot is controlled in real time.
And (3) loop iteration: and (3) carrying out loop iteration in a new control period, re-determining the system state, carrying out model prediction, solving the optimization problem, and updating the control instruction in real time until the expected motion of the mobile robot is realized. The model prediction control is an iterative optimization process, and loop iteration needs to be carried out in each control period, so that the state is estimated again in each period, model prediction is carried out, the optimization problem is solved, and the control instruction is updated in real time until the expected motion of the mobile robot is realized.
The objective function of the model predictive control is as follows:
wherein s is a synovial function,e is the system state deviation, e=x des -x cur X represents the system state, i.e. [ x ] b ,y b ,θ b ,θ 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ,θ 6 ] T ，(x b ,y b ) Represents the planar position of the moving base, represents the coordinates in the x-axis and the y-axis, respectively, θ b Representing the yaw angle of the mobile base, i.e. the angle by which the mobile base rotates about its vertical axis, (θ) 1 ,θ 2 ,θ 3 ,θ 4 ,θ 5 ,θ 6 ) Is the joint angle of the mechanical arm, x des X is the desired system state cur For the current system state, P, Q, R is a positive weighting matrix, N is the control time domain, u i For system input at time i in the future, i.e. [ v ] b,x ,v b,y ,ω b ,ω 1 ,ω 2 ,ω 3 ,ω 4 ,ω 5 ,ω 6 ] T ，(v b,x ,v b,y ) Representing the speed, ω, of movement of the moving base along the x-axis and the y-axis, respectively b Representing the angular velocity of rotation of the mobile base, i.e. the angular velocity of rotation of the mobile base about its vertical axis, (ω) 1 ,ω 2 ,ω 3 ,ω 4 ,ω 5 ,ω 6 ) Is the joint angular velocity of the mechanical arm, u eq For synovial equivalent control, i.e. ignoring uncertainty and interference, the approach ratio of the sliding mode function s is:
wherein epsilon, delta, alpha and beta are all control parameters, alpha >0, 0< beta <1.
By setting the objective function, the robustness of the control system can be enhanced, the influence of uncertainty such as parameter disturbance, external disturbance, modeling error and the like is suppressed, the control system is kept stable and reliable in an uncertain or complex environment, quick and accurate control is realized, the control system is prompted to quickly respond to a control target, the error is quickly regulated and eliminated, and the system output is enabled to be closer to an expected value. Meanwhile, the approach law of the sliding film function is improved, so that the sliding film function can reach the vicinity of a sliding mode surface quickly, and buffeting is reduced. Parameters in the objective function can be optimized through experiments and debugging, so that the optimal control performance is obtained.
Constraints of model predictive control refer to constraints imposed on system states, control inputs, or other related variables. These constraints are set to ensure that the control system meets the requirements of the actual application and system performance during operation. Constraints in the present invention include system state constraints, control input constraints, and dynamics constraints. The system state constraint is a limitation set on state variables such as the position, the posture, the speed and the like of the mechanical arm or the moving base, for example, the joint angle of the mechanical arm should be kept within a safe range, the positions of the moving base and the mechanical arm should be limited in a working area and the like; control input constraints, which are limitations set on the actuator output or control commands of the robotic arm and motion base, for example, the magnitude of the control input should be limited within the rated range of the motor to avoid damaging the motor or equipment. The system state constraints and the control input constraints include:
x i+1 =f(x i ,u i ) I.e. x i+1 Is x i And u i Functions of (2), e.g. x i+1 =Ax i +Bu i ，x i The system state at the moment i;
x i e, X, i=0, … …, N-1, X is the system state constraint set;
u i e U, i=0, … …, N-1, U is the system input constraint set.
In addition to system state constraints and control input constraints, the present embodiment also sets slip film shrinkage constraints and kinetic constraints. The slip film shrinkage constraint is:eta is shrinkage, eta is [0,1 ]. The control system can be more quickly close to a control target through the contraction constraint of the sliding film, and errors can be quickly adjusted and eliminated, so that expected control is realized.
The dynamic constraint, namely, the limitation on the actual movement of the mechanical arm and the moving base is set according to the dynamic performance of the mechanical arm and the moving base, so that the control system is helped to keep stable, the performance of the control system is optimized, the control system is better adapted to the actual application requirements, the control precision and the control efficiency are improved, and the mechanical arm or the moving base is prevented from being damaged or collided.
The movable base is generally heavy in weight and slow in dynamic response, and the mechanical arm is light in weight, fast in dynamic response and higher in control precision, so that great difference exists between the dynamic performance of the movable base and the dynamic response. The invention redesigns the dynamic constraint conditions of the moving base and the mechanical arm, wherein the dynamic constraint conditions of the moving base are as follows:
v b ≤v b max ，v b to move the translation speed of the base, v b max Maximum translation speed for the mobile base;
the method comprises the steps of carrying out a first treatment on the surface of the Wherein phi is b For the weight coefficient, d is the horizontal distance from the end effector to the task target, d b A threshold value for the horizontal distance of the end effector to the task target, which is proportional to the size of the operating space of the manipulator, v low The value of the speed lower limit of the movable base can be 0; v high Is the high speed limit for moving the base.
The kinetic constraints of the mechanical arm are:
ω k ≦ω k max ，ω k angular velocity, ω, of the kth joint of the mechanical arm k max Maximum angular velocity for the kth joint;
wherein k is a natural number between 1 and 6, i.e. one or more joints of the mechanical arm can be selected for dynamic constraint, lambda k As the weight coefficient omega k low The value of the angular velocity lower limit of the kth joint is 0; omega k high An angular velocity upper limit for the kth joint; p is the distance from the end effector to the task target, p max The threshold value, which is the distance of the end effector to the task target, is proportional to the size of the operating space of the robotic arm.
The dynamic constraints on the motion base and the robotic arm may be used separately or in combination in different embodiments or applications, respectively. When the mechanical arm is far away from the target, the maximum speed value of the moving base is large, so that rapid translational movement is realized, and meanwhile, the maximum speed of the mechanical arm is low (the value can be 0), so that the mechanical arm is kept still; as the robot approaches the task target quickly, and the task target is in the optimal working interval of the mechanical arm, the maximum speed of the movable base is reduced, so that the movable base is kept stable, and meanwhile, the maximum speed of the mechanical arm is increased quickly, so that the operation is started; when the end effector of the robotic arm is less than the collision threshold from the target, the maximum speed of the robotic arm should be rapidly reduced to prevent collisions.
The various methods described above, in some embodiments, may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device via the ROM and/or the communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more actions or steps of the method described above may be performed. The computer program product may include a computer readable storage medium having computer readable program instructions embodied thereon for performing aspects of the present disclosure. The computer readable storage medium may be a tangible device that can hold and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing.
The foregoing is a further detailed description of the present application in connection with specific/preferred embodiments, and it is not intended that the practice of the present application be limited to such descriptions. It will be apparent to those skilled in the art to which the present application pertains that several alternatives or modifications can be made to these described embodiments without departing from the spirit of the invention, and that these alternatives or modifications should be considered to be within the scope of the present application.
Claims (7)
1. A mobile robot control method based on constraint model predictive control comprises the following specific steps:
modeling a system: performing kinematic modeling on a mobile robot comprising a mobile base and a mechanical arm;
state estimation: determining a real-time state of the mobile robot;
model predictive control: based on a kinematic model and a real-time state of the mobile robot, predicting future system states and behaviors by using model prediction control, solving a control problem by minimizing an objective function and meeting constraint conditions to obtain optimal control input in a future control time domain, and controlling the motion of the mobile robot in real time;
and (3) loop iteration: performing loop iteration in a new control period, re-determining the system state, performing model prediction, solving the optimal control input, and updating the control instruction in real time until the expected motion of the mobile robot is realized;
wherein the constraint conditions of model predictive control include dynamic constraints on the robotic arm and/or the mobile base; the kinetic constraints of the mobile base are:
v b ≤v b max ；
；
wherein v is b To move the translation speed of the base, v b max Maximum translation speed for the mobile base; phi (phi) b For the weight coefficient, d is the horizontal distance from the end effector to the task target, d b Threshold, v, for horizontal distance of end effector to task target low A lower speed limit for moving the base; v high A high speed limit for moving the base;
the kinetic constraints of the mechanical arm are:
ω k ≦ω k max ；
；
where k is the number of the selected joint of the mechanical arm, ω k Angular velocity, ω, of the kth joint of the mechanical arm k max Is the maximum angular velocity of the kth joint of the mechanical arm lambda k Is the weight coefficient omega of the kth joint of the mechanical arm k low The angular velocity of the kth joint of the mechanical arm is the lower limit; omega k high As the kth jointAn angular velocity high limit; p is the distance from the end effector to the task target, p max A threshold value that is a distance of the end effector to the task target;
the constraint conditions also comprise system state constraint and control input constraint, and specifically comprise:
x i+1 =f(x i ,u i )，x i the system state at the moment i;
x i e, X, i=0, … …, N-1, X is the system state constraint set;
u i e U, i=0, … …, N-1, U is the system input constraint set.
2. The mobile robot control method based on constrained model predictive control as claimed in claim 1, wherein d b Proportional to the size of the operating space of the mechanical arm.
3. The mobile robot control method based on constrained model predictive control as claimed in claim 1, wherein v low Is 0.
4. The mobile robot control method based on constrained model predictive control as claimed in claim 1, wherein p max Proportional to the size of the operating space of the mechanical arm.
5. The mobile robot control method based on constrained model predictive control as claimed in claim 1, wherein ω is k low Is 0.
6. The mobile robot control method based on constrained model predictive control according to claim 1, wherein the objective function of the model predictive control is:
where g is the position and pose deviation of the end effector, g=q des -q cur Q tableShowing the position and pose of the end effector, q des For the target position pose of the end effector, q cur For the real-time position and pose of the end effector, P, Q, R is a positive weighting matrix, N is a control time domain, u i Is the system input at time i in the future.
7. A computer-readable storage medium, characterized in that a computer program is stored thereon, which computer program is executed by a processor for performing the steps of the method according to any of claims 1-6.
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