Versatile Reactive Bipedal Locomotion Planning Through Hierarchical Optimization

When experiencing disturbances during locomotion, human beings use several strategies to maintain balance, e.g. changing posture, modulating step frequency and location. However, when it comes to the gait generation for humanoid robots, modifying step time or body posture in real time introduces nonlinearities in the walking dynamics, thus increases the complexity of the planning. In this paper, we propose a two-layer hierarchical optimization framework to address this issue and provide the humanoids with the abilities of step time and step location adjustment, Center of Mass (CoM) height variation and angular momentum adaptation. In the first layer, times and locations of consecutive two steps are modulated online based on the current CoM state using the Linear Inverted Pendulum Model. By introducing new optimization variables to substitute the hyperbolic functions of step time, the derivatives of the objective function and feasibility constraints are analytically derived, thus reduces the computational cost. Then, taking the generated horizontal CoM trajectory, step times and step locations as inputs, CoM height and angular momentum changes are optimized by the second layer nonlinear model predictive control. This whole procedure will be repeated until the termination condition is met. The improved recovery capability under external disturbances is validated in simulation studies.