Reactive bipedal balance: Coordinating compliance and stepping through virtual model imitation for enhanced stability

Compliance and step location adjustments are both important for robots to maintain balance when encountering external disturbances. Compared with controlling separately, unifying compliance with step location adjustments and integrating them into real-time pattern planning gets obvious advantages. However, the controllers’ models differ significantly from each other and from the dynamics of real position-controlled robots, compromising the stabilizing performance. In this paper, we propose a Virtual Model Imitation (VMI) strategy that unifies the controllers’ models and aligns them with actual robot dynamics. Based on this, a reactive pattern planning method is proposed which simultaneously coordinates compliance and step location adjusting strategies. The approach involves emulating the passive dynamic motion of a Linear Inverted Pendulum Model (LIPM) to enable the robot to respond to external disturbances with compliant motions automatically. Additionally, Zero Moment Point Intervened (ZI) estimation is employed to precisely determine the Center of Mass (CoM) state. Real-time optimization of step location is then conducted to stabilize the estimated CoM, actively responding to external disturbances. Importantly, the decision to adjust step location is quantitatively defined. To enhance efficiency, explicit solutions for both ZI Estimation and Step Location Optimization are provided to reduce computational costs. To validate our approach, we conducted simulations and experiments using the biped robot BHR-T, subjecting it to unexpected external pushes and obstacles during walking.