Biped robot uneven road walking planning and control method

Abstract

The present application belongs to the technical field of robot control, and discloses a walking planning and control method of a biped robot on uneven ground, which comprises the following steps: 1, constructing a gait generator, activating the gait generator when switching the support phase, generating the center of mass and the expected trajectory of the swing leg of the next support phase based on a simplified linear inverted pendulum model; 2, constructing a whole-body controller, activating the whole-body controller in each control cycle, integrating the current center of mass and the expected state of the swing leg, the expected posture of the body and other task space targets, and solving the optimal moment output. The present application explores the application of the "step strategy" in robot disturbance resistance, integrates the landing time into the optimization on the basis of optimizing the landing position, so that when the robot encounters a large disturbance, the robot can restore balance through a fast swing leg, thereby improving the disturbance resistance and robustness of the robot, and the planning method is combined with the whole-body motion controller, and is successfully applied to walking on uneven ground.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of robot control, and particularly relates to a walking planning and control method for a biped robot on uneven ground. BACKGROUND

[0002] The biped robot has been developed to date and basically realizes stable walking on flat ground or structural terrain, but under the existing planning and control framework, its anti-disturbance performance is weak when walking on uneven ground, and the robustness is still poor, which limits its application in outdoor scenes and some special industrial scenes. How to realize stable walking of the biped robot on uneven ground has very important significance for its further practical application.

[0003] At present, in the related researches at home and abroad, the control methods for walking on uneven ground are as follows: on the one hand, the priori of the terrain is obtained through deep visual perception, laser radar scanning and the like, but in outdoor scenes, the light intensity, topography and other factors often cause large errors, thereby affecting the stability of walking; on the other hand, the situation of the ground supportable area is estimated through active sensing of the pressure distribution of the foot bottom, but the sensing accuracy is often a main factor affecting the stability, and the walking speed and dynamics are also limited. In addition, in addition to active detection, some researches add certain damping and compliance in the process of landing of the swing foot, but the anti-disturbance ability is still very limited. In the researches on walking on flat ground, in order to maintain balance in the disturbance, the "ankle strategy", "hip strategy" and "step strategy" have been successively excavated, among which the "step strategy" shows the greatest anti-disturbance ability. Similar behaviors are also obvious when humans walk. The conventional step strategy is mostly dependent on the linear characteristics of the simplified model under fixed support time, and only adjusts the step position, and it cannot timely step to restore balance when facing large disturbance. And there is no related strategy applied to walking on uneven ground. SUMMARY

[0004] The present application aims to provide a walking planning and control method for a biped robot on uneven ground, to solve the technical problem that the step strategy cannot timely step to restore balance when facing large disturbance.

[0005] To solve the above technical problem, the specific technical scheme of the walking planning and control method for a biped robot on uneven ground is as follows:

[0006] A walking planning and control method for a biped robot on uneven ground, comprising the following steps:

[0007] Step 1: constructing a gait generator, activating the gait generator when switching the support phase, generating the center of mass and the expected trajectory of the swing foot of the next support phase based on a simplified linear inverted pendulum model;

[0008] Step 2: Construct a whole-body controller, activate the whole-body controller in each control cycle, integrate the current center of mass and swing leg desired state, body desired posture, etc. task space target, and solve the optimal moment output.

[0009] Further, the step 1 constructs a gait generator, including the following steps:

[0010] Step 1.1: Given the desired walking parameters, construct an ideal walking cycle unit according to the simplified linear inverted pendulum model with the current support foot position as the origin, and obtain the desired final state of the current support phase and the next support phase as the reference quantity of the optimization target;

[0011] Step 1.2: Capture the robot state at the support phase switching time, and obtain the initial state of the current support phase center of mass plane position and velocity according to the joint state estimation, and make a first-order approximation of the analytical solution of the linear inverted pendulum model about the support time to obtain a linear representation about the support time;

[0012] Step 1.3: Define the feasible landing area of the swing foot, organize it into a convex domain surrounded by linear inequality constraints, and finally, the error between the final state of the current and next support phase and the desired final state is taken as the cost function, and the landing position and time of the current support phase are taken as the optimization variables, to construct a quadratic programming problem, and solve to obtain the optimal landing time and position of the swing foot in the current support phase;

[0013] Step 1.4: After obtaining the optimal landing position and time, take the current center of mass state as the initial value, generate the center of mass position and velocity trajectory of the current support phase according to the linear inverted pendulum analytical solution; plan the swing foot trajectory with a cubic Bezier curve to guide it to the desired landing position; then, the center of mass and swing foot trajectory adopts a redundancy strategy, and a section of uniform speed descending trajectory is appended after the trajectory in the expected landing time period, which actively guides the swing foot to the possible "pit" when there is a large drop on the ground. Further, the step 1.1 includes the following specific steps:

[0014] Nominal forward step s x And nominal lateral step s y , construct an ideal walking cycle unit according to the simplified linear inverted pendulum model with the current support foot position as the origin, and obtain the desired final state of the current support phase and the next support phase as:

[0015]

[0016] Where, ξ d,c And ξ d,n are the desired center of mass plane states of the current step and the next step, which are determined by the set walking parameters, S≡sinh(T sup / T c ), C≡cosh(T sup / T c ), T sup is the nominal support time.

[0017] Further, the step 1.2 is linear representation of support time as:

[0018]

[0019] where, is the center of mass planar state, and further predict the final state of the center of mass in the current support phase and the next support phase according to the above formula:

[0020]

[0021] where, ξ(0) is the initial center of mass state of the current support phase captured when the gait generator is called, and the support time of the next support phase is set to the nominal support time T sup in this step prediction, I2 is a unit matrix;

[0022] The coefficient matrix T(t) and U(t) come from the analytical solution of the linear inverted pendulum: ξ(t) = T(t)ξ(0) + U(t)p Foot , and the coefficient matrix and B come from the first order approximation of the analytical solution to time, there is a relationship: Further, the step 1.3 is constructed as follows:

[0023]

[0024] s.t.(-1) sgn ·[0 1]·p Foot ≥l min (1)

[0025]

[0026] where, Q c and Q n are the error weight coefficients of the current step and the next step predicted state; l min is the minimum lateral step distance; l max is the maximum stride radius; t c and are the upper and lower bounds of the allowed support time; indicate different support phases.

[0027] Further, the step 2 whole body controller is constructed as follows:

[0028]

[0029]

[0030] -τ max ≤τ≤τ max (6)

[0031] where q is the generalized position, v is the generalized velocity, τ is the driving torque, is the optimization variable, ρ C indicates the contact force, g task is the task space cost function, including the desired center of mass and swing leg trajectory tracking tasks, pelvis and torso posture holding tasks, etc., Φ task is the target quantity in the task space; J task is the Jacobian matrix in the joint space corresponding to the task quantity; is the desired second order quantity in the task space under PD control, k p , task and k d,task are the corresponding position and velocity gains, Φ d,task and are the desired target quantity and first order target quantity, Q task is the weight matrix of the task space target; represents the joint space target, S is the selection matrix of the specified joint, and the position and velocity targets in the joint space are integrated into the desired acceleration command by the PD control q′ d and are the desired position and velocity of the specified joint, k p,J and k d,J are the corresponding position and velocity gain matrices; is the energy cost, and Q τ are the corresponding weight matrices; equation (4) describes the robot dynamics constraint, M(q) is the inertia matrix, B is the driving mapping matrix, C(q, v) contains the Coriolis force, centrifugal force term, g(q) is the gravity term, equation (5) describes the support foot contact keeping constraint, contains the position and posture acceleration of the support foot, J CF is the velocity Jacobian of the support foot, k d,CFis the contact damping coefficient; the ideal reachable radius constraint forms a circular domain, and the support foot contact keeps the constraint (5) is an inscribed regular n-polygon approximation to the circular domain to form a linear constraint, and formula (6) describes the maximum torque constraint that can be output by each joint of the robot.

[0032] Further, the step 2 dynamics constraint (4) constructs the contact model of the foot bottom as a distributed point contact, and the "friction cone" of each contact point is further approximated as an "inscribed friction pyramid", and the contact force of each contact point is is expressed as a positive combination of the base vectors of the inscribed friction pyramid: where R f(i) is the orientation of the contact foot, is a set of base vectors of the friction pyramid, is the weight of the base vector, and P i =R f(i) β is the contact mapping matrix of the contact point. The velocity Jacobian matrix J C (q) of the dynamics constraint is composed of the velocity Jacobian matrices of each contact point:

[0033]

[0034] The contact mapping matrix P(w) is composed of the mapping matrices of each contact point:

[0035]

[0036] Further, the ideal reachable radius constraint forms a circular domain, and the support foot contact keeps the constraint (5) is an inscribed regular n-polygon approximation to the circular domain to form a linear constraint.

[0037] The uneven road walking planning and control method of the biped robot has the following advantages: the application of the "step strategy" in robot disturbance resistance is further explored, and on the basis of optimizing the landing position, the landing time is further integrated into the optimization, so that when the robot encounters a large disturbance, the robot can restore balance through rapid leg swinging, improving the disturbance resistance and robustness of the robot, and the planning method is combined with the whole body motion controller, and is successfully applied to uneven road walking. The application scene of the method is not limited to uneven road walking, and the application of the method to flat ground walking can also greatly improve the disturbance resistance of the robot. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a schematic diagram of a nominal planar center of mass trajectory generated by a pre-existing inverted pendulum model under certain walking parameters;

[0039] Figure 2 is a schematic diagram of a swing foot landing feasible region constructed under linear inequality constraints;

[0040] Figure 3 This is a schematic diagram of the trajectory planning of the swinging foot, which includes "Bezier" curve segments and linear segments;

[0041] Figure 4 This is a schematic diagram of the contact model between the sole of the foot and the ground. DETAILED DESCRIPTION

[0042] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a biped robot walking planning and control method on uneven roads in conjunction with the accompanying drawings.

[0043] A bipedal robot walking planning and control method on uneven surfaces based on foot placement and timing adjustment strategy, including the construction of a "gait generator" and a "whole-body controller":

[0044] First, the construction of the "Gait Generator" includes the following steps:

[0045] Step 1: If Figure 1 As shown, p0 is the current support foot position, which is also the origin of the center of mass planning for each step, p1 and p2 are the next step sequence, s x and s y is the preset forward and lateral step length. The curve in the figure is the ideal center of mass plane trajectory. Given the desired walking parameters, the nominal forward step length s x and nominal lateral step length s y , taking the current supporting foot position as the origin, an ideal walking cycle unit is constructed according to the simplified linear inverted pendulum model, and the expected final states of the current supporting phase and the next supporting phase are obtained as the reference quantity for the subsequent optimization objectives.

[0046]

[0047] Among them, ξ d,c and ξ d,n is the expected center of mass plane state of the current step and the next step, which is determined by the set walking parameters. is the dynamic characteristic time of the linear inverted pendulum model, S≡sinh(T sup / T c ), C≡cosh(T sup / T c ), T sup is the nominal support time.

[0048] Step 2: Capture the robot state at the moment of support phase switching, and estimate the initial state of the center of mass plane position and velocity of the current support phase based on the joint state. Make a first-order approximation of the analytical solution of the linear inverted pendulum model with respect to the support time, and obtain a linear representation of the support time:

[0049]

[0050] where, is the centroid plane state, and the final state of the current support phase and the next support phase are predicted according to the above formula:

[0051]

[0052] where, is the initial centroid state of the current support phase captured when the gait generator is called. Moreover, to avoid the nonlinear coupling between the next support phase decision time and the current support phase decision time, the support time of the next support phase is set to the nominal support time T sup in this step prediction.

[0053] The coefficient matrices T(t) and U(t) come from the analytical solution of the linear inverted pendulum: ξ(t) = T(t)ξ(0) + U(t)p Foot , and the coefficient matrices and B come from the first-order approximation of the analytical solution with respect to time, and there is a relationship:

[0054]

[0055] Step three: the feasible foot placement region for the swing leg is demarcated, which is organized as a convex region surrounded by linear inequality constraints. Finally, the error between the final state of the current and next support phases and the desired final state is taken as the cost function, and the foot placement position and time of the current support phase are taken as the optimization variables, and the following quadratic programming problem is constructed to obtain the optimal foot placement time and position of the swing leg in the current support phase.

[0056]

[0057] s.t.(-1) sgn ·[0 1]·p Foot ≥l min (1)

[0058]

[0059] where, Q c and Q n are the error weight coefficients of the current step and the next step predicted state; l min is the minimum lateral step distance; l max is the maximum stride radius; t c and are the upper and lower bounds of the allowed support time; Indicate different support phases. The feasible region surrounded by constraints (1) and (2) is shown as Figure 2 p1 is the current support foot position, p2 is a point within the swing foot landing feasible region, and l min is the minimum lateral step distance, and l max is the maximum step radius, the circle formed by the step radius is approximated by an octagon inscribed in it. The constraint of the minimum lateral step distance is mainly to prevent the swing foot from stepping on the current support foot and tripping the robot itself; the constraint of the maximum reachable radius mainly considers the kinematic limit of the robot.

[0060] Step four: after obtaining the optimal landing position and time, the mass center position and velocity trajectory of the current support phase are generated based on the linear inverted pendulum analytical solution with the current mass center state as the initial value; the swing foot trajectory is planned using a cubic Bezier curve to guide it to the desired landing position; then, the mass center and swing foot trajectories use a redundancy strategy to append a uniformly descending trajectory after the trajectory in the desired landing time period, actively guiding the swing foot to the possible "pit" when there is a large drop in the ground. An example of swing foot planning is shown in Figure 3 , where p0 and p3 are the current position and the target position of the swing foot obtained by optimization, respectively, and p1 and p2 are the intermediate control points. Here, p2 is set above p3 so that the swing foot has a vertical landing speed, avoiding the phenomenon of slipping. In Figure 3 , p0 and p3 are the start and end points of the "Bezier" curve, p1 and p2 are the intermediate control points, and an additional trajectory is appended after the Bezier curve, which maintains the final speed of the Bezier curve segment to continue guiding the swing foot downward.

[0061] Further, in each control cycle, the whole body controller is activated to integrate the mass center and swing foot desired states, body desired posture, and other task space targets issued by the "gait generator", to solve the optimal torque output. The whole body controller is constructed as follows:

[0062]

[0063] -τ max ≤τ≤τ max (6)

[0064] where q is the generalized position, v is the generalized velocity, τ is the driving torque, is the optimization variable, ρC indicates the contact force, g task is the task space cost function, including the desired mass center and swing foot trajectory tracking tasks, pelvis and torso posture maintenance tasks, etc. Φ task is the target quantity in the task space; J task is the Jacobian matrix in the joint space corresponding to the task quantity; is the task space desired second order quantity under PD control, k p , task and k d,task are the corresponding position and velocity gains, Φ d,task and are the desired target quantity and first order target quantity, Q task is the weight matrix of the task space target; denotes the joint space target, S is the selection matrix of the specified joints, the position and velocity target of the joint space are integrated by the PD control into the desired acceleration command q′ d and are the desired position and velocity of the specified joints, k p,J and k d,J are the corresponding position and velocity gain matrices; is the energy cost, which intends to reduce the energy consumption while facilitating the stable and effective solution of the quadratic programming problem, and Q τ are the corresponding weight matrices; (4) describes the robot dynamics constraint, M(q) is the inertia matrix, B is the driving mapping matrix, C(q, v) contains the Coriolis force, centrifugal force term, g(q) is the gravity term, the dynamics constraint (4) constructs the contact model of the foot bottom as a distributed point contact (as shown in Figure 4 , f Ci is the ground contact force at the support point, its friction cone is linearly approximated by the inscribed quadrangular pyramid, n i is the normal force, β ij is the base vector of the friction pyramid), the "friction cone" of each contact point is further approximated as an "inscribed friction pyramid", the contact force of each contact point is expressed as a positive combination of the base vectors of the inscribed friction pyramid: where R f(i) is the orientation of the contact foot, is the set of base vectors of the friction pyramid, is the weight of the base vector, P i = R f(i) β is the contact mapping matrix of the contact point. The velocity Jacobian matrix J C (q) of the dynamics constraint of the contact point is composed of the velocity Jacobian matrix of each contact point:

[0065]

[0066] The contact mapping matrix P(q) is composed of the mapping matrix of each contact point:

[0067]

[0068] (5) describes the support foot contact keeping constraint, Jkis the position and pose acceleration of the support foot, CF is the velocity Jacobian of the support foot, d,CF is the contact damping coefficient; the ideal reachable radius constraint forms a circular region, and the support foot contact keeping constraint (5) is an inscribed regular n-polygon approximation of the circular region to form a linear constraint.

[0069] It can be understood that the present application is described by some embodiments, and those skilled in the art know that various changes or equivalent replacements can be made to the features and embodiments without departing from the spirit and scope of the present application. In addition, under the guidance of the present application, the features and embodiments can be modified to adapt to specific conditions and materials without departing from the spirit and scope of the present application. Therefore, the present application is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of the present application are within the scope of the present application.

Claims

1. A method for planning and controlling bipedal robot walking on uneven surfaces, characterized in that: The steps include: Step 1: Build a gait generator. When the stance phase switches, activate the gait generator and generate the center of mass and the expected trajectory of the swing foot in the next stance phase based on a simplified linear inverted pendulum model. Step 1.1: Given the desired walking parameters, construct an ideal walking cycle unit based on the simplified linear inverted pendulum model with the current stance position as the origin. Obtain the desired final states of the current stance phase and the next stance phase, which serve as reference quantities for subsequent optimization objectives. Step 1.2: Capture the robot state at the moment of support phase switching and estimate the initial state of the center of mass plane position and velocity of the current support phase based on the joint state. Make a first-order approximation of the analytical solution of the linear inverted pendulum model with respect to the support time to obtain a linear representation of the support time. Step 1.3: Define the feasible landing area for the swinging foot and organize it into a convex domain bounded by linear inequality constraints. Finally, use the error between the final state of the current and next support phases and the desired final state as the cost function, and use the landing position and time of the current support phase as optimization variables to construct a quadratic programming problem to solve and obtain the optimal landing time and position of the swinging foot in the current support phase. Step 1.3 constructs the following quadratic programming problem to solve and obtain the optimal landing time and position of the swing foot in the current stance phase: s.t.(-1) sgn ·[0 1]·p Foot ≥l min (1) Among them, Q c and Q n is the error weight coefficient between the current step and the next step prediction state; l min is the minimum lateral step; l max is the maximum step radius; t c and are the upper and lower bounds of the allowed support time; Indicates different support phases; Step 1.4: After obtaining the optimal landing position and time, the center of mass position and velocity trajectory for the current support phase are generated using the current center of mass state as the initial value based on the analytical solution of the linear inverted pendulum. The swinging foot trajectory is planned using a cubic Bezier curve to guide it to the desired landing position. Then, a redundant strategy is used for the center of mass and swinging foot trajectory, adding a uniform descent trajectory after the desired landing time period. When there is a large drop in the ground, the swinging foot is actively guided towards a possible "pit". Step 2: Construct a whole-body controller. In each control cycle, activate the whole-body controller, integrate the task space goals of the current center of mass, the desired state of the swinging foot, and the desired body posture, and solve for the optimal torque output.

2. The method for planning and controlling bipedal robot walking on uneven surfaces according to claim 1, characterized in that: The step 1.1 includes the following specific steps: Nominal forward step length s x and nominal lateral step length s y , taking the current support foot position as the origin, an ideal walking cycle unit is constructed according to the simplified linear inverted pendulum model, and the expected final states of the current support phase and the next support phase are obtained as follows: Among them, ξ d,c and ξ d,n is the expected center of mass plane state of the current step and the next step, which is determined by the set walking parameters. is the dynamic characteristic time of the linear inverted pendulum model, S≡sinh(T sup / T c ), C≡cosh(T sup / T c ), T sup is the nominal support time.

3. The method for planning and controlling bipedal robot walking on uneven surfaces according to claim 1, characterized in that: The linear expression of the support time in step 1.2 is: in, is the center of mass plane state, and then the center of mass final state of the current support phase and the next support phase is predicted according to the above formula: in, ξ(0) is the initial center of mass state of the current stance phase captured when the gait generator is called. The support time of the next stance phase is set to the nominal support time T in the step prediction. sup , I2 is the unit matrix; The coefficient matrices T(t) and U(t) come from the analytical solution of the linear inverted pendulum: ξ(t) = T(t)ξ(0) + U(t)p Foot , and the coefficient matrix and B come from the first-order approximation of the analytical solution to time, and there is a relationship:

4. The method for planning and controlling bipedal robot walking on uneven surfaces according to claim 1, characterized in that: The whole body controller of step 2 is constructed as follows: -t max ≤τ≤τ max (6) Where q is the generalized position, v is the generalized velocity, τ is the driving torque, is the optimization variable, ρ C Indicated contact force, g task is the task space cost function, including the expected center of mass and swing foot trajectory tracking task from the gait generator, pelvic and torso posture maintenance task, Φ task is the target quantity in the task space; J task is the joint space Jacobian matrix corresponding to the task volume; is the expected second-order quantity of the task space obtained under PD control, k p,task and k d,task are the corresponding position and velocity gains, Φ d,task and is the desired target quantity and the first-order target quantity, Q task is the weight matrix of the task space target; Represents the joint space target, S is the selection matrix for the specified joint, and the position and velocity targets in the joint space are integrated into the desired acceleration command by PD control q′ d and is the desired position and velocity of the specified joint, k p,J and k d,J are the corresponding position and velocity gain matrices; For energy consumption cost, and Q τ is the corresponding weight matrix; Formula (4) describes the robot dynamic constraints, M(q) is the inertia matrix, B is the drive mapping matrix, C(q,v) includes the Coriolis force and centrifugal force terms, g(q) is the gravity term, Formula (5) describes the support foot contact maintenance constraint, Contains the position and attitude acceleration of the supporting foot, J CF is the velocity Jacobi of the supporting leg, k d,CF is the contact damping coefficient; the ideal reachable radius constraint forms a circular domain, and the support foot contact maintenance constraint (5) is an inscribed regular n-gon approximation of the circular domain to form a linear constraint. Formula (6) describes the maximum torque constraint that each joint of the robot can output.

5. The method for planning and controlling bipedal robot walking on uneven surfaces according to claim 4, characterized in that: The step 2 dynamic constraint (4) constructs the contact model of the sole of the foot as a distributed point contact, and the "friction cone" of each contact point is further approximated as an "inscribed friction pyramid". The contact force of each contact point is Expressed as a positive combination of the basis vectors of the inscribed friction pyramid: where R f(i) For the direction of the contact foot, is the set of friction pyramid basis vectors, is the weight of the basis vector, P i =R f(i) β is the contact mapping matrix of the contact point, and the contact point velocity Jacobian matrix J of the dynamic constraint C (q) is composed of the velocity Jacobian matrices of each contact point: The contact mapping matrix P(q) is composed of the mapping matrices of the contact points:

6. The method for planning and controlling bipedal robot walking on uneven surfaces according to claim 5, characterized in that: The ideal reachable radius constraint forms a circular domain, and the support foot contact maintenance constraint (5) is an approximation of an inscribed regular n-gon of the circular domain to form a linear constraint.

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