CN105608309A - Biped robot walking plan and control method - Google Patents

Abstract

The invention provides a biped robot walking plan and control method. The method comprises the steps of establishing an equivalent model of a robot; determining a phase change graph meeting the requirement of the equivalent model; determining a phase change graph of a single-step horizontal movement track according to a human gait walking formula, namely, calculating a relationship between the speed of a single step and the step length/period of the single step; calculating a foothold according to the horizontal movement track of the single step; and controllably converting the position of the calculated foothold into an angle required for finishing motion of each joint. According to the method, the human gait formula is associated with the relationship between the walking speed and the step length/period of the single step, so that the calculation of the step length/period of the single step can be simplified; the period of the single step serves as a trigger event of single-step starting and ending, so that the end speed of the single step can be well predicted and the real-time calculation and adjustment of the foothold can be facilitated; and based on the motion description of the phase change graph, the analysis of a motion law of the biped robot can be more visual.

Description

A kind of biped robot's walking planning and control method

Technical field

The present invention relates to a kind of biped robot's walking planning and control method.

Background technology

Biped robot promises to be the robot type of serving people in the environment of human lives and work most,It is robot field's study hotspot always. Although biped robot's research has in recent years obtained huge progress, just at presentDevelopment level see, be also far from being able to the requirement of practical application, one of the main reasons is exactly the dynamic motion of robotAbility and Ability of Resisting Disturbance are all poor.

Walking ability is the essential motion feature that biped robot is different from other types mobile robot, all the time,Walking planning is exactly one of emphasis of biped robot's research. Current most biped robots' walking planning is all full(ZeroMomentPoint is called for short: ZMP) under the prerequisite of scleronomic constraint condition, generate joint time-based foot point of zero momentMovement locus sequence, joint is accurately carried out these track sequences and is completed walking movement. In this case, biped robot is oneDetermine system, do not have uncontrollable free degree. ZMP scleronomic constraint itself is also a kind of too conservative method, and it requires to prop upSpike contacts completely with ground, and the mankind are in the actual motion process such as walking and running, do not observe ZMP criterion. In addition,Biped robot for part without sole, owing to being a unactuated joint between shank and ground, the motion in this joint is notControlled, therefore the walking planing method based on joint trajectories sequence has been difficult to be suitable for.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of biped robot's walking planning and control of using phase transformation figureMethod processed,

A kind of biped robot's walking planning and control method, is characterized in that it comprises the following steps:

(1) set up the dynamical equations that meets biped robot's equivalent model, determine the phase transformation figure of stable state track;

(2) calculate the single step gait parameter that biped robot walks, in phase transformation figure, determine the single step horizontal movement of expectingTrack;

(3) calculate according to horizontal movement track the foothold that biped robot walks, realize horizontal movement speed and switch, andCarry out in real time calculating and the adjustment of foothold;

(4) according to the each joint angles of foothold position calculation, and control each joint and complete walking movement;

Described phase transformation figure is taking biped robot's horizontal level x as transverse axis, biped robot's horizontal movement speedFor verticalAxle.

Further, it is by calculating dummy level power and setting up the described dynamical equations of robot health, and according toRelation between this calculating robot's body levels movement velocity and horizontal level.

Further, it determines according to people's walking step state formula the single step cycle that biped robot's speed of travel is correspondingAnd step-length, set up the dynamical equations of robot health, and computing machine person single step average level movement velocity accordinglyAnd relation between horizontal foothold position.

Further, resolve the described body levels equation of motion, and according to stable state walking movement pattern at the uniform velocity, determine and expectSingle step initial foothold position and single step initial velocity, according to the single step cycle, in phase transformation figure, be depicted as desired speed correspondenceHorizontal movement track.

Further, according to the body levels equation of motion of resolving, the level while obtaining speed of travel switching is initially stopped overPoint position, completes the switching of the speed of travel; According to robot present level foothold position, present level movement velocity and currentStep is estimated the end speed of current step remaining time; And calculate in real time next step foothold position according to the end speed of estimating.

Further, according to foothold position, calculate and lead leg each joint angles and send to joint control, then convertBecome to support each joint moment and send to joint control; Joint control applies control to the each joint of robot on request, lastComplete biped robot's walking movement.

Further, it by fictitious force control, the equivalence of the biped robot when standing becomes a linear inverted pendulum systemSystem; Described linear reversible pendulum system is that barycenter is controlled at perseverance by total body center of mass height design closed-loop control rate by vertical fictitious forceTake the altitude, is robot body posture design closed-loop control rate by virtual moment, and health robot pose is remained on uprightlyState, determines virtual vertical power and virtual moment.

Owing to adopting numerical procedure of the present invention, the motion that the present invention is based on phase transformation figure is described, can intuitive analysis bipedThe characteristics of motion of robot. By the associated speed of travel of body gait formula and the relation in single step step-length/cycle, can simplify listThe calculating in length/cycle step by step. Biped robot's attitude and highly can carry out closed-loop control by fictitious force, the speed of travel canCarry out closed-loop control with the foothold adjustment by real-time, the directive motion state of robot can be effectively controlled,And the trigger event that starts and finish using the single step cycle as single step, can fine single step end speed be predicted, be convenient toReal-time calculating and the adjustment of pin point, therefore the walking movement of robot has very strong robustness, can offset robot itselfThe impact of the factors such as frictional damping, also can outer force-disturbance and the original motion state of fast quick-recovery when the out-of-flatness disturbance of ground.

Brief description of the drawings

Fig. 1 a: biped robot's fictitious force control model schematic diagram.

Fig. 1 b: the model schematic diagram of the corresponding linear reversible pendulum system of biped robot.

Fig. 2: biped robot's horizontal movement phase transformation figure.

Fig. 3: the aspiration level movement locus that target velocity is corresponding.

Fig. 4: the speed of travel is switched schematic diagram.

Fig. 5: flow chart of the present invention.

Detailed description of the invention

Below in conjunction with accompanying drawing, technical solution of the present invention is described in detail.

Step S1: be robot target setting horizontal movement speed and health height on host computer.

Step S2: almost maintain constant feature with reference to health height and attitude in mankind's walking process, pass through fictitious forceControl and become a linear reversible pendulum system (LinearInverted without sole biped robot equivalence when standingPendulumModel, is called for short: LIPM), as shown in Figure 1 b. One of key character of LIPM is exactly that total body center of mass remains atConstant altitude z_d, body posture remains at upright posture. Therefore be, that total body center of mass height design closes by vertical fictitious forceBarycenter is controlled at constant altitude by ring control rate, body posture protected for body posture designs closed-loop control rate by virtual momentBe held in erectility.

The closed-loop control rate of total body center of mass height is:

$F_z=k_{zp}(z-z_d)+k_{zd}\stackrel{\·}{z}+mg---\left(1\right)$

In formula: z andBe respectively actual total body center of mass height and vertical speed, m is body quality, and g is that gravity acceleratesDegree, k_zpAnd k_zdBe respectively ratio and the differential parameter of vertical closed-loop control rate.

The closed-loop control rate of body posture is:

${\mathrm{\τ}}_b=k_{bp}{\mathrm{\θ}}_b+k_{bd}{\stackrel{\·}{\mathrm{\θ}}}_b---\left(2\right)$

In formula: θ_bWithBe respectively actual body posture angle and attitude angular velocity, k_bpAnd k_bdBeing respectively rotatablely moves closesRatio and the differential parameter of ring control rate.

Step S3: under the effect of formula (1) and (2) two closed-loop control rates of formula, the height of health and attitude can be fineMaintain desired value, therefore when stabilized walking planning, the vertical fictitious force size that health maintains constant altitude to be needed is bodyThe gravity F that body is subject to_z=mg, but direction is contrary with gravity direction; The virtual moment that health maintains upright posture to be needed is zero, τ_b=0. In virtual vertical power and the definite situation of virtual moment, the horizontal movement of calculating dummy level power and setting up robot healthEquation is:

$\stackrel{\·\·}{x}={\mathrm{\ω}}^{2}x---\left(3\right)$

In formula:

$\mathrm{\ω}=\sqrt{\frac{g}{z_d}}$

The orbital energy of LIPM is:

$E_{LIP}=\frac{1}{2}{\stackrel{\·}{x}}^2-\frac{1}{2}{\left(\mathrm{\ω}x\right)}^2---\left(4\right)$

The orbital energy E of robot_LIPDuring single step, remain unchanged, obtain body levels movement velocity and horizontal movementRelation between position:

${\stackrel{\·}{x}}^2={\mathrm{\ω}}^2{x}^2+2E_{LIP}---\left(5\right)$

According to formula (5), and draw taking horizontal level x as transverse axis, horizontal movement speedFor the robot level fortune of the longitudinal axisMoving phase transformation figure, and represent all horizontal stable states that meet with the straight line of a stable orbit by name in the drawings'sSet, as shown in Figure 2.

Step S4: the phase transformation figure by horizontal movement knows, it is constant that body levels movement velocity can not keep, and therefore definition is singleThe average level movement velocity of step is the single step speed of travel:

$\stackrel{\‾}{\stackrel{\·}{x}}=\frac{\mathrm{\λ}}{T_{ds}}---\left(6\right)$

In formula:For single step average level movement velocity, λ is single step step-length, T_dsFor the single step cycle.

Reference man's walking step state formula is determined single step cycle and the step-length that single step average level movement velocity is corresponding, andLand the single step cycle as supporting leg and liftoff trigger event.

Single step step-length is:

$\mathrm{\λ}=0.58{\stackrel{\‾}{\stackrel{\·}{x}}}^{0.3}{z_h}^{0.7}---\left(6\right)$

In formula: z_hFor hip joint terrain clearance.

The single step cycle is:

$T_{ds}=0.58\frac{{z_h}^{0.7}}{{\stackrel{\‾}{\stackrel{\·}{x}}}^{0.7}}---\left(7\right)$

Step S5: for desirable at the uniform velocity stable state walking movement, the horizontal movement speed amount of having a net increase of of its single step should be 0,The initial velocity of single stepWith end speedUnanimously, according to phase transformation figure symmetry feature, the initial velocity of single step and end speedDegree is the same, the initial foothold position x of single step₀With end position x_fOpposite number each other. Step-length λ is known, and the initial bit of single stepPut and end position opposite number each other, can determine that the single step initial position of expectation is:

$x_0=-\frac{\mathrm{\λ}}{2}---\left(8\right)$

The body levels equation of motion of analytic expression (3), obtains:

$\left[\begin{array}{c}x\left(t\right)\\ \stackrel{\·}{x}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cosh \left(\mathrm{\ω}t\right)& \frac{\sin h\left(\mathrm{\ω}t\right)}{\mathrm{\ω}}\\ \mathrm{\ω}\sinh \left(\mathrm{\ω}t\right)& \cosh \left(\mathrm{\ω}t\right)\end{array}\right]\left[\begin{array}{c}{x}_0\\ {\stackrel{\·}{x}}_0\end{array}\right]---\left(9\right)$

In formula: x₀WithBe respectively initial foothold position and the initial velocity of single step, i.e. the original state of single step.

The single step initial position of expectation is brought into the body levels equation of motion of having resolved, just can be determined the single step of expectationInitial velocity is:

${\stackrel{\·}{x}}_0=-\frac{\mathrm{\ω}\[1+\cosh \left({\mathrm{\ωT}}_{ds}\right)\]}{\sinh \left({\mathrm{\ωT}}_{ds}\right)}{x}_0---\left(10\right)$

The original state of now single step can be determined, just can in phase transformation figure, be depicted as and expect speed according to the single step timeSpend corresponding horizontal movement track, as shown in Figure 3.

Step S6: step period T is adjusted in order_{t_ds}For current step period T_{e_ds}With expectation step period T_{d_ds}Average, by basisThe horizontal end speed that present speed is correspondingThe horizontal initial rate corresponding with desired speedBring the horizontal movement after parsing intoIn equation, just can obtain the initial foothold of the level position x that adjusts step_{t_0}，

$x_{t\_0}=\frac{{\stackrel{\·}{x}}_{t\_f}-\cosh \left({\mathrm{\ωT}}_{t\_ds}\right){\stackrel{\·}{x}}_{t\_0}}{\mathrm{\ω}\sinh \left({\mathrm{\ωT}}_{t\_ds}\right)}---\left(11\right)$

Adjust step and land and just can complete the switching of horizontal movement speed according to this horizontal initial position, as shown in Figure 4.

Step S7: the frictional damping loss of robot itself, outer force-disturbance and ground out-of-flatness all can change robotMotion state, cause motion actual and that expect to have error, this method is according to robot present level position x_c, current waterFlat speedWith current step T remaining time_remEstimate the end speed of current step

${\stackrel{\·}{x}}_{est\_f}=\mathrm{\ω}\sinh \left({\mathrm{\ωT}}_{rem}\right)x_c+\cosh \left({\mathrm{\ωT}}_{rem}\right)---\left(12\right)$

Step S8: calculate in real time next step foothold x according to the end speed of estimating_{n_0}，

$x_{n\_0}=\frac{{\stackrel{\·}{x}}_{n\_f}-\cosh \left({\mathrm{\ωT}}_{n\_ds}\right){\stackrel{\·}{x}}_{est\_f}}{\mathrm{\ω}\sinh \left({\mathrm{\ωT}}_{n\_ds}\right)}---\left(13\right)$

The final impact of any disturbance is the impact on current step end speed, and the real-time foothold control method of this method alsoCan well recover the movement velocity that robot is expected, complete disturbance rejection control.

Step S9: according to next step foothold position x_{n_0}, calculate and lead leg each joint angles and send to joint controlDevice, is converted into the each joint moment of support according to force Jacobian matrix by fictitious force and sends to joint control.

Step S10: joint control applies control to the each joint of robot on request, finally completes biped robot's walkingMotion.

The above be only the detailed description of the invention in the present invention, but protection scope of the present invention is not limited to this, appointsThe people what is familiar with this technology, in the technical scope of institute of the present invention dewfall, can understand conversion or the replacement expected, all should be encompassed inOf the present invention comprise scope within.

Claims (7)

1. biped robot's walking planning and a control method, is characterized in that it comprises the following steps:

(1) set up the dynamical equations that meets biped robot's equivalent model, determine the phase transformation figure of stable state track;

(2) calculate the single step gait parameter that biped robot walks, in phase transformation figure, determine the single step horizontal movement track of expecting;

(3) calculate according to horizontal movement track the foothold that biped robot walks, realize horizontal movement speed and switch, and in real timeCarry out calculating and the adjustment of foothold;

(4) according to the each joint angles of foothold position calculation, and control each joint and complete walking movement;

Described phase transformation figure is with biped robot's horizontal levelFor transverse axis, biped robot's horizontal movement speedFor the longitudinal axis.

2. a kind of biped robot's walking planning as claimed in claim 1 and control method, is characterized in that:

It is by calculating dummy level power and setting up the described dynamical equations of robot health, and the computing machine person accordinglyRelation between body horizontal movement speed and horizontal level.

3. a kind of biped robot's walking planning as claimed in claim 2 and control method, is characterized in that:

It determines according to people's walking step state formula single step cycle and the step-length that biped robot's speed of travel is corresponding, sets up machineThe dynamical equations of the device person, and computing machine person single step average level movement velocity and horizontal foothold position accordinglyRelation between putting.

4. a kind of biped robot's walking planning as claimed in claim 3 and control method, is characterized in that:

Resolve the described body levels equation of motion, and according to stable state walking movement pattern at the uniform velocity, determine that the single step of expecting initially fallsPin point position and single step initial velocity according to the single step cycle, are depicted as the horizontal movement rail that desired speed is corresponding in phase transformation figureMark.

5. a kind of biped robot's walking planning as claimed in claim 4 and control method, is characterized in that:

According to the body levels equation of motion of resolving, the initial foothold of the level position while obtaining speed of travel switching, completes rowWalk the switching of speed;

Estimate current step remaining time according to robot present level foothold position, present level movement velocity and current stepEnd speed; And calculate in real time next step foothold position according to the end speed of estimating.

6. a kind of biped robot's walking planning as claimed in claim 5 and control method, is characterized in that:

According to foothold position, calculate and lead leg each joint angles and send to joint control, then be converted into the each joint of supportMoment sends to joint control;

Joint control applies control to the each joint of robot on request, finally completes biped robot's walking movement.

7. a kind of biped robot's walking planning as claimed in claim 1 and control method, is characterized in that:

By fictitious force control, the equivalence of the biped robot when standing becomes a linear reversible pendulum system for it; Described linear handstandOscillator system is that barycenter is controlled at constant altitude by total body center of mass height design closed-loop control rate by vertical fictitious force, by virtualMoment is robot body posture design closed-loop control rate, and health robot pose is remained on to erectility, determines virtual perpendicularStraight power and virtual moment.