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  Gait disturbance balance control method for bipedal robot under stochastic uncertainty environment

  Wang Yanjun


(School of Information Engineering, Xi'an Eurasia University, Xi'an 710065, China)

Abstract


Abstract:In a random and uncertain environment, bipedal robots need to adjust their gait in real time to maintain balance. At the same time, the control system needs to have good stability to ensure that the robot will not lose its balance or be damaged when it is disturbed, which puts forward high requirements for the performance of the control algorithm. In order to improve the stability of robot motion, a gait disturbance balance control method for bipedal robots in stochastic and uncertain environment was proposed. The real-time attitude of the bipedal robot is obtained through the RCG attitude solving algorithm, and the monopedal phase stage, bipedal phase stage and foot ankle joint trajectory are generated according to the attitude information, and the above trajectory is taken as the ideal trajectory, and the adaptive synovial membrane controller is designed to deal with the external disturbance caused by the random and uncertain environment, and the control parameters and strategies are dynamically adjusted so that the robot can walk stably according to the ideal trajectory, so as to realize the gait disturbance balance control of the bipedal robot. Experimental results show that the proposed method can significantly improve the stability and adaptability of the robot under environmental disturbance, and significantly improve the stability of the robot's movement. Keywords: bipedal robot; RCG attitude solving; Gait trajectory generation; adaptive synovial membrane controller; Gait balance controlCLC Number: TP242 Document Identification Code: A Article Number: 1001-9944(2024)11-0047-04

Gait Disturbance Balance Control Method for Bipedal Robot in Stochastic Un－ certain Environments

WANG Yanjun（School of Information Engineering，Xi’an Eurasia University，Xi＇an 710065，China）


Abstract：In a stochastic and uncertain environment，bipedal robot need to adjust their gait in real－time to maintain balance． At the same time，the control system needs to have good stability to ensure that the robot does not lose bal－ ance or suffer damage when disturbed，which puts high demands on the performance of control algorithms． In order to improve the stability of robot motion，a gait disturbance balance control method for bipedal robot in stochastic uncertain environments is proposed． Real－time pose of the bipedal robot is obtained through the RCG pose calculation algorithm． Based on the pose information，single legged phase，bipedal phase，and ankle joint trajectories are generated，and the above trajectories are used as ideal trajectories． An adaptive sliding film controller is designed to handle external dis－ turbances caused by random and uncertain environments． Control parameters and strategies are dynamically adjusted to enable the robot to walk steadily according to the ideal trajectory，thereby achieving gait disturbance balance control of the bipedal robot． The experimental results show that the proposed method can significantly improve the stability and adaptability of robot under environmental disturbances，and significantly enhance the stability of robot motion．

Key words：bipedal robot； RCG attitude calculation； gait trajectory generation； adaptive synovial controller； gait balance control

As a robot that highly simulates human walking, the adaptability and stability of the bipedal robot in the complex environment are particularly obvious

Significant. However, due to the inherent instability of the walking system of the bipedal robot, coupled with the various disturbances that may be encountered in practical applications
收稿日期:2024-05-16;修订日期 :2024-09-18
基金项目:陕西省计算机教育学会项目(JSJXH-1904)
作者简介:王艳君(1975-),女,硕士,副教授,研究方向为软件开发, 机器人。

How to ensure its stability and balance in the process of walking has become an urgent problem to be solved, such as uneven ground and external interference. Therefore, it is necessary to study an effective gait disturbance balance control method for bipedal robots.

At present, the research on gait control methods of bipedal robots is constantly being explored and optimized, aiming to improve the stability and adaptability of bipedal robots in the face of complex environments and disturbances. Ref. [1] combined the deep Q network algorithm with deterministic strategy gradient optimization Double-Q network to be applied to gait control of bipedal robots, however, there are still problems with poor control performance in this study. Ref. [2] proposes a method of adaptive robust control combined with multi-objective parameter optimization, but its control performance still needs to be enhanced in extremely uncertain environments. In Ref. [3], gait control of bipedal robots was realized by combining the spring inverted pendulum model and the whale swarm algorithm, but the convergence of the algorithm is limited, and environmental disturbance may affect the gait control effect. In Ref. [4], a model-free heuristic gait template control is proposed to generate gait trajectories and adjust them to achieve stable walking, but the control stability of the model-free method needs to be improved due to the lack of prior knowledge.

In order to further improve the control effect, this method fully considers the random uncertain environmental conditions, and designs a gait disturbance balance control method for bipedal robots, in order to improve the motion balance and stability of the robot.

  1. Design of a gait disturbance balance control method

  1.1 Bipedal robot attitude solving


In order to provide real-time and accurate robot attitude data to the control system, so that it can respond quickly in the event of disturbance and maintain the stable walking of the robot. Firstly, the attitude of the bipedal robot was calculated to make effective adjustments in time when the disturbance occurred, so as to reduce the risk of the robot falling and improve the walking performance and safety of the robot. In the attitude calculation, the RCG attitude solution algorithm is used to separate the gravity and acceleration components, and the acceleration data is converted to the world coordinate system through the direction cosine matrix.

The acceleration value measured by the accelerometer is the superposition a ′ a ′ a^(')a^{\prime} of the acceleration of gravity H H HH and the acceleration of the motion of the bipedal robot, which is expressed as
a n = H n + a ′ ω Φ a n = H n + a ′ ω Φ a_(n)=H_(n)+a^(')omega Phia_{n}=H_{n}+a^{\prime} \omega \Phi

where: ω ω omega\omega is the angular velocity data collected by the gyroscope; Φ Φ Phi\Phi In order to reduce the drift caused by the accumulation of errors, the angular acceleration data and the Kalman filter are used [ 5 − 6 ] [ 5 − 6 ] ^([5-6]){ }^{[5-6]} to adjust the angle data Φ Φ Phi\Phi to obtain the corrected angle value Φ ′ Φ ′ Phi^(')\Phi^{\prime} .
  When the bipedal robot moves, the body may tilt, at this time

The direction of the accelerometer will also change, resulting in a rotation angle θ θ theta\theta , and the direction of gravity will also change, therefore, the effect of gravity needs to be eliminated to obtain the true acceleration of the bipedal robot body in all directions, which is calculated as
a n ′ = a n ω − Φ ′ θ a n ′ = a n ω − Φ ′ θ a_(n)^(')=a_(n)omega-Phi^(')thetaa_{n}^{\prime}=a_{n} \omega-\Phi^{\prime} \theta

Since the coordinate system ( X , Y , Z ) ( X , Y , Z ) (X,Y,Z)(X, Y, Z) of the accelerometer measurement data ( X ′ , Y ′ , Z ′ ) X ′ , Y ′ , Z ′ (X^('),Y^('),Z^('))\left(X^{\prime}, Y^{\prime}, Z^{\prime}\right) is not the same as the world coordinate system, the coordinate system conversion is performed using the directional cosine matrix [ 7 ] [ 7 ] ^([7]){ }^{[7]} . The roll angle ϕ ϕ phi\phi , pitch angle θ θ theta\theta and heading angle between the two coordinate systems are calculated by integrating the gyroscope data β β beta\beta , and the specific conversion process is as follows:
{ X ′ = X cos ⁡ ( ϕ ) + Y sin ⁡ ( ϕ ) sin ⁡ ( θ ) − Z sin ⁡ ( ϕ ) cos ⁡ ( θ ) Y ′ = Y cos ⁡ ( ϕ ) + Z sin ⁡ ( θ ) Z ′ = X sin ⁡ ( ϕ ) − Y sin ⁡ ( θ ) cos ⁡ ( ϕ ) + Z cos ⁡ ( θ ) cos ⁡ ( ϕ ) X ′ = X cos ⁡ ( ϕ ) + Y sin ⁡ ( ϕ ) sin ⁡ ( θ ) − Z sin ⁡ ( ϕ ) cos ⁡ ( θ ) Y ′ = Y cos ⁡ ( ϕ ) + Z sin ⁡ ( θ ) Z ′ = X sin ⁡ ( ϕ ) − Y sin ⁡ ( θ ) cos ⁡ ( ϕ ) + Z cos ⁡ ( θ ) cos ⁡ ( ϕ ) {[X^(')=X cos(phi)+Y sin(phi)sin(theta)-Z sin(phi)cos(theta)],[Y^(')=Y cos(phi)+Z sin(theta)],[Z^(')=X sin(phi)-Y sin(theta)cos(phi)+Z cos(theta)cos(phi)]:}\left\{\begin{array}{l} X^{\prime}=X \cos (\phi)+Y \sin (\phi) \sin (\theta)-Z \sin (\phi) \cos (\theta) \\ Y^{\prime}=Y \cos (\phi)+Z \sin (\theta) \\ Z^{\prime}=X \sin (\phi)-Y \sin (\theta) \cos (\phi)+Z \cos (\theta) \cos (\phi) \end{array}\right.

Through the above formula, the current posture of the bipedal robot can be accurately perceived, including the acceleration and angle information relative to the world reference frame, if these attitude angles change drastically or exceed the normal range, it may be a manifestation of the robot's instability, which is essential for subsequent gait trajectory planning and balance control.

  1.2 Bipedal robot gait trajectory generation


After obtaining accurate acceleration and angle information, the foot motion trajectory and centroid movement path are generated according to the walking requirements and environmental conditions of the robot.

  1.2.1 Generate ZMP trajectories for the monoped phase phase


The world coordinate system of the bipedal robot ( X ′ , Y ′ , Z ′ ) X ′ , Y ′ , Z ′ (X^('),Y^('),Z^('))\left(X^{\prime}, Y^{\prime}, Z^{\prime}\right) is converted into a local coordinate system relative to the current walking direction and standing plane of the robot ( x , y , z ) ( x , y , z ) (x,y,z)(x, y, z) , and the zero-moment point (ZMP) trajectory of the monoped phase stage is calculated by a three-dimensional linear inverted model in this coordinate system [ 8 − 9 ] [ 8 − 9 ] ^([8-9]){ }^{[8-9]} , and the calculation formula is as follows
{ x ¨ = e 2 ( x − s x ) y ¨ = e 2 ( y − s y ) z ¨ = e 2 ( z − s z ) x ¨ = e 2 x − s x y ¨ = e 2 y − s y z ¨ = e 2 z − s z {[x^(¨)=e^(2)(x-s_(x))],[y^(¨)=e^(2)(y-s_(y))],[z^(¨)=e^(2)(z-s_(z))]:}\left\{\begin{array}{l} \ddot{x}=e^{2}\left(x-s_{x}\right) \\ \ddot{y}=e^{2}\left(y-s_{y}\right) \\ \ddot{z}=e^{2}\left(z-s_{z}\right) \end{array}\right.

where: s x , s y , s z s x , s y , s z s_(x),s_(y),s_(z)s_{x}, s_{y}, s_{z} is the displacement; x ¨ , y ¨ , z ¨ x ¨ , y ¨ , z ¨ x^(¨),y^(¨),z^(¨)\ddot{x}, \ddot{y}, \ddot{z} is the acceleration of displacement; e e ee is the natural frequency.

  1.2.2 Generate bipedal phase ZMP trajectories


According to the continuity of the attitude information of the bipedal robot, the ZMP trajectory of the bipedal phase stage is obtained by using the fifth polynomial interpolation method:
S d i ( t ) = a 0 + a 1 t + a 2 t 2 + a 3 t 3 + a 4 t 4 + a 5 t 5 S d i ( t ) = a 0 + a 1 t + a 2 t 2 + a 3 t 3 + a 4 t 4 + a 5 t 5 S_(d)^(i)(t)=a_(0)+a_(1)t+a_(2)t^(2)+a_(3)t^(3)+a_(4)t^(4)+a_(5)t^(5)S_{\mathrm{d}}^{i}(t)=a_{0}+a_{1} t+a_{2} t^{2}+a_{3} t^{3}+a_{4} t^{4}+a_{5} t^{5}

where: a 0 , a 1 , a 2 , a 3 , a 4 , a 5 a 0 , a 1 , a 2 , a 3 , a 4 , a 5 a_(0),a_(1),a_(2),a_(3),a_(4),a_(5)a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5} is the polynomial coefficient [ 10 ] ; S d i ( t ) [ 10 ] ; S d i ( t ) ^([10]);S_(d)^(i)(t){ }^{[10]} ; S_{\mathrm{d}}^{i}(t) is bipedal

The trajectory of the centroid of the phase in the first i i ii cycle.

  1.2.3 Generate foot ankle trajectories


The movement of the ankle joint is essential for the efficient walking of the bipedal robot, and the expected ankle movement usually includes two aspects: position and posture, and the position refers to the coordinates of the ankle joint in space, which can be ( x , y , z ) ( x , y , z ) (x,y,z)(x, y, z) represented by the local coordinate system mentioned above. The pose describes the rotation of the ankle joint relative to a reference coordinate system, and the attitude is described by using Euler angles, such as α α alpha\alpha the rotation angles of the x , y , z x , y , z x,y,zx, y, z axes are , β , γ β , γ beta,gamma\beta, \gamma , then the pose can be expressed as ( α , β , γ ) ( α , β , γ ) (alpha,beta,gamma)(\alpha, \beta, \gamma) .

According to the above-mentioned generated monoped phase stage ZMP trajectory, bipedal phase stage ZMP trajectory and foot ankle joint trajectory, the walking gait trajectory of the bipedal robot is finally generated.

  1.3 Gait disturbance balance control implementation


In the actual environment, the bipedal robot may face uncertain factors such as uneven ground, excessive external impact force, or changes in the robot's own parameters, which may make the actual posture and gait trajectory of the robot deviate from the expectation, causing the robot to lose balance. Therefore, gait disturbance balance control was implemented for the robot attitude solution results and the generated gait trajectory.

An adaptive synovial membrane controller was designed, and the gait disturbance control strategy of the bipedal robot based on the controller is shown in Figure 1.
  Figure 1 Block diagram of the adaptive synovial membrane controller
Fig． 1 Block diagram of adaptive sliding membrane controller

  1.3.1 Control goal setting


Firstly, according to the attitude solution results of the bipedal robot above, the instability state of the robot is judged, and at the same time, in order to avoid the common flutter problem in synovial control, the adaptive synovial membrane controller is designed to make the gait trajectory of the robot converge to close to the ideal trajectory, for any step of the robot i i ii , a synovial condition is defined, and when the state of the robot satisfies the synovial condition, the gait of the robot is considered to be close enough to the ideal trajectory:
s ˙ ( t ) s ( t ) < 0 s ˙ ( t ) s ( t ) < 0 s^(˙)(t)s(t) < 0\dot{s}(t) s(t)<0

Eq. (6) means that s ( t ) s ( t ) s(t)s(t) the derivative of the synovial surface is opposite to s ( t ) s ( t ) s(t)s(t) itself, thus ensuring that the state of the system converges towards the synovial surface.

  1.3.2 Controller Settings


Based on the above control objectives, the bipedal robot is estimated in the first k k kk step

The amplitude f f ff F ^ F ^ hat(F)\hat{F} of the external disturbance caused by the uncertain environment is uncertain, and ‖ f ‖ < F ^ ‖ f ‖ < F ^ ||f|| < hat(F)\|f\|<\hat{F} using the amplitude and the dynamical vector, Ψ Ψ Psi\boldsymbol{\Psi} the controller outputs are calculated:
u = s ( t ) w ¨ d + J v ( w , w ˙ ) − F v Ψ − F ^ u = s ( t ) w ¨ d + J v ( w , w ˙ ) − F v Ψ − F ^ u=s(t)w^(¨)_(d)+J_(v)(w,w^(˙))-F_(v)Psi- hat(F)u=s(t) \ddot{w}_{\mathrm{d}}+J_{\mathrm{v}}(w, \dot{w})-\boldsymbol{F}_{\mathrm{v}} \boldsymbol{\Psi}-\hat{F}

where: w ¨ d w ¨ d w^(¨)_(d)\ddot{w}_{\mathrm{d}} is the state of a joint of the robot; F v F v F_(v)\boldsymbol{F}_{\mathrm{v}} is an inertial matrix; J v ( w , w ˙ ) J v ( w , w ˙ ) J_(v)(w,w^(˙))J_{\mathrm{v}}(w, \dot{w}) for Coriolis and gravity terms; Ψ Ψ Psi\boldsymbol{\Psi} is a dynamic vector that describes the dynamics of the robot when the controller outputs it.

In order to ensure the convergence of the controller, assuming that the f f ff actual amplitude of the external disturbance is F m F m F_(m)F_{\mathrm{m}} , the maximum perturbation value is , f m f m f_(m)f_{\mathrm{m}} and F ^ F ^ hat(F)\hat{F} the minimum value of the amplitude estimate is f ^ m f ^ m hat(f)_(m)\hat{f}_{\mathrm{m}} , and f r = f m / f ^ m f r = f m / f ^ m f_(r)=f_(m)// hat(f)_(m)f_{\mathrm{r}}=f_{\mathrm{m}} / \hat{f}_{\mathrm{m}} the following convergence iterative formula is designed:
B 1 = ( a n − a n ′ ) { ( u ∣ ‖ h ‖ ⩽ f r ) } B 1 = a n − a n ′ u ∣ ‖ h ‖ ⩽ f r B_(1)=(a_(n)-a_(n)^(')){(u∣||h|| <= f_(r))}B_{1}=\left(a_{n}-a_{n}^{\prime}\right)\left\{\left(u \mid\|h\| \leqslant f_{\mathrm{r}}\right)\right\}
  where: h h hh is the feedback input.

The bipedal robot walks according to the gait trajectory in the random uncertainty environment, and if the external disturbance amplitude is estimated to be small, the controller increases h h hh the modulus of the feedback input by the above formula, so as to compensate for the influence that the disturbance brings; Conversely, if the amplitude of the external disturbance is too large, the controller will adaptively reduce h h hh the modulus of the feedback input to avoid overcompensation, in this way, the controller can maintain a stable balance control effect in the case of different disturbances in a random and uncertain environment.

  2 Experiments and Analysis


In order to verify the overall effectiveness of the gait disturbance balance control method of bipedal robot in stochastic and uncertain environment, it is necessary to test it.

The BHR-6S bipedal robot was selected as the test object, the robot is about 45 cm high, the mass without the shell is about 2.1 kg, the mass with the shell is about 2.3 kg, the feet, hands, and the head contain 2 degrees of freedom respectively 12 , 6 12 , 6 12,612, ~ 6 , and it is equipped with a single camera, gyroscope and plantar pressure sensing sensors.

The Kalman filter is set to have a sampling period of 0.26 s, a solution frequency of 50 Hz, a fixed step size limit of 0.04 m, a fixed step width limit of 0.05 m, a maximum pitch angle of the start/stop stage 2 ∘ 2 ∘ 2^(@)2^{\circ} , a gait period of 2 s, a maximum swing leg height of 0.1 m, a synovial surface width of 0.02 m, a safety boundary threshold of attitude angle ± 5 ∘ ± 5 ∘ +-5^(@)\pm 5^{\circ} , and a position error of ± 0.02 m ± 0.02 m +-0.02m\pm 0.02 \mathrm{~m} .

Simulate a continuously varying uneven ground experimental environment ± 4 mm ± 4 mm +-4mm\pm 4 \mathrm{~mm} within the height difference, so that the bipedal robot walks 20 steps according to the target trajectory at a 0.03 m / s 0.03 m / s 0.03m//s0.03 \mathrm{~m} / \mathrm{s} speed, and in the process, the walking results of the robot before and after the proposed method are compared without the gait disturbance balance control strategy, as shown in Figure 2.

As can be seen from Fig. 2, after adopting the control strategy of the proposed method, the walking speed of the robot on the uneven ground is stably maintained at 0.03 m / s 0.03 m / s 0.03m//s0.03 \mathrm{~m} / \mathrm{s} about that, indicating that the stability of the proposed method is strong.