Online Gait Planning And Control For Humanoid Robots Based On Multiple Strategies Integration

Human beings can realize stable walking in various scenes such as the uneven ground and the narrow space by coordinating body posture.Furthermore,it is often necessary to adjust the gait parameters in real-time so as to maintain balance when faced with external disturbances.Inspired by these phenomena,by considering the redundant design of the Degree of Freedom(Do F)of humanoid robots,researchers try to exploit various walking strategies,including ankle strategy,stepping strategy(step duration and step location adjustment),hip strategy(body inclination angle/spin angular momentum change)and height variation strategy(modulation of the height of Center of Mass(Co M)),to enhance the walking stability and adaptability in real-world environments.Due to the large constraints arisen from the structural size,actuation capability,double-feet support zone and other limitations,how to realize the optimization and the integration of various walking strategies has become the current research hotspot.However,the high non-linearity and strong coupling of the bipedal walking system bring great challenges to the implementation of gait planning and stability control algorithms.On the one hand,how to establish a reasonable and efficient model of constrained optimization for an individual strategy still needs further study.On the other hand,there is still a lack of a general gait planning framework that can integrate all the above walking strategies.This paper aims to solve the above problems and conducts following studies:Firstly,the theory of multi-strategy walking stability is studied,and the overall optimization framework for integrating various balance strategies is proposed.By analyzing the principle of human walking,the basic concepts of bipedal walking,including step duration,step length,step width,the Centre of Pressure(Co P)and Zero-Moment-Point(ZMP)are defined.Through learning from the research results of bionics,typical walking balance strategies are introduced,including ankle strategy,stepping strategy,hip strategy and Co M height variation strategy.Subsequently,by using the ZMP-based stability criterion and the concept of the orbit energy,the relationships among the above strategies and walking stability are systematically revealed in the way of qualitative and quantitative analysis,which provide the theoretical guidelines for online gait adjustment.After then,focusing on coupling effect and high nonlinearity caused by the exploitation of balance strategies,this paper proposes to adopt the nonlinear constrained optimization algorithms to solve the balance strategies,by taking into account physical constraints.Following the routine that the basic step parameters such as the step duration and the step location are firstly determined and then the other state variables including Co M height and body inclination angles are adjusted,this paper proposes the overall framework to realize the integration of various walking strategies.Secondly,the online optimization algorithm for step duration adaptation and step location adjustment is studied.Based on the Three-dimensional(3D)Linear Inverted Pendulum(LIP)model,the analytical expression about the Co M motion is derived.Then,after introducing the implicit time variables which alternate the time-related hyperbolic functions,the linear relationship of the Co M among the implicit time variables is established.To track the desired centroid state(position and velocity)at the end of each step cycle,the cost function that can make use of stepping strategy is proposed.Through considering the feasibility constraints,including these on the variation range of step parameters,the tolerant velocity of the swing leg and the variation range of the acceleration of Co M,the mathematical model for the nonlinear constrained optimization is established.Through changing the reference target and constraint conditions,this model can realize the fast switch between single-step prediction and two-steps prediction as well as relative position tracking and absolute position tracking.By using the Sequential Quadratic Programming(SQP)algorithm,the above optimization problems can be solved quickly.As a result,the step duration and step location and be adjusted online.The results of the simulation evaluation on the gait optimization and the results of virtual prototype experiments demonstrate that the algorithm can meet the requirement of real-time computation.Besides,it can help to accomplish the non-periodic walking tasks that require the simultaneous change of step duration and location.Furthermore,this algorithm can enhance the recovery capability from omnidirectional pushes.Thirdly,the online optimization algorithm for body inclination angle and Co M height adjustments is studied.By taking jerks of the Co M position and the body inclination angles as control inputs,the prediction model of the Co M motion and the body rotational motion is established.Based on the 3D Inverted Pendulum plus Flywheel(IPF)model,this work proposes a cost function that can integrate hip strategy and height variation strategy,with the aim of tracking the Co M states(position,velocity and acceleration)and body rotation states(angle,angular velocity and angular acceleration)during the predictive horizon.By restricting the ZMP within the foot support polygon as well as considering the feasibility constraints including these on the variation range of leg length,the mathematical model for the Nonlinear Model Predictive Control(NMPC)is established.Again,the SQP algorithm is employed to solve the constrained optimization problem in a fast manner.It turns out that the optimal ZMP position,step location,body inclination angle and Co M height can be obtained simultaneously by solving the optimization problem.The simulation evaluations on the gait optimization and the virtual prototype experiments demonstrate that the algorithm can meet the requirement of real-time computation.Besides,the algorithm contributes to accomplish the challengeable walking tasks such as climbing stairs and passing the space with limited height.Furthermore,it can also enhance the recovery capability from omnidirectional pushes.Finally,the hierarchical control algorithm based on the integration of multiple walking strategies is proposed.By taking the nonlinear programming that exploits the stepping strategy as the first layer and taking the NMPC that exploits other strategies as the second layer,a hierarchical optimization algorithm is established,which can adjust the Co M trajectory,body inclination angles and step parameters online.Then,after planning the feasible swing leg trajectory,the planning of complete gait is realized.By taking into account the effect of body rotation and Co M movement on the walking system,this paper proposes an algorithm for distributing ground reactive force/torque.After then,by designing the admittance controllers for Co M position tracking,foot height compensation and body inclination angle modulation,the whole-body posture control is realized.At last,through integrating the tracking control of joint angles,a layered control structure consisting of the gait planning layer,the posture modulation layer and the servo tracking layer is built.The simulation evaluations demonstrate that the gait plan layer can realize the integration of ankle strategy,stepping strategy,hip strategy and Co M height variation strategy.Thus,it can help to accomplish the non-periodic walking tasks that require the simultaneous change of step duration,step location and Co M height.Meanwhile,the generated ZMP positions approach closer to the support center.Compared with the algorithms that merely use one of the balance strategies or merely integrated a part of these strategies,the integration of all the balance strategies can further enhance the recovery capability from omnidirectional pushes.By using the Nao-H25 robot,the paper also conducts hardware experiments on multiple scenarios,including stable walking with time-varying parameters,stable walking on flat grounds of different materials,maintaining balance on slope terrains,walking through narrow space with limited height and recovery from external pushes.The experimental results demonstrate that the algorithm proposed here can enhance the stability and adaptability of bipedal walking in real-world scenarios.This study systematically analyzes the influence of common balance strategies on the stability of bipedal walking and realizes online gait planning and control based on multistrategy integration.In the long run,this work provides support for the practical application of humanoid robots.