Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model

Abstract

This study presents a theoretical method for planning and controlling agile bipedal locomotion based on robustly tracking a set of non-periodic keyframe states. Based on centroidal momentum dynamics, we formulate a hybrid phase-space planning and control method that includes the following key components: (i) a step transition solver that enables dynamically tracking non-periodic keyframe states over various types of terrain; (ii) a robust hybrid automaton to effectively formulate planning and control algorithms; (iii) a steering direction model to control the robot's heading; (iv) a phase-space metric to measure distance to the planned locomotion manifolds; and (v) a hybrid control method based on the previous distance metric to produce robust dynamic locomotion under external disturbances. Compared with other locomotion methodologies, we have a large focus on non-periodic gait generation and robustness metrics to deal with disturbances. This focus enables the proposed control method to track non-periodic keyframe states robustly over various challenging terrains and under external disturbances, as illustrated through several simulations.

DRS-LIP: Linear Inverted Pendulum Model for Legged Locomotion on Dynamic Rigid Surfaces

“…One of the most widely studied reduced-order model for stationary surface locomotion is the linear inverted pendulum (LIP) model [8], which models a legged robot as a point mass atop a massless leg. Although the LIP does not capture the complete robot dynamics, many of today's legged robots can be relatively accurately described by the LIP, including bipeds [9], [10] and quadrupeds [4], [11]. This is because they typically have a heavy upper body and lightweight legs.…”

“…The DRS-LIP is valid under the assumption that the actual robot's rate of whole-body angular momentum about the CoM is negligible (assumption (A1)). To relax this assumption, the point mass of the proposed DRS-LIP could be augmented with a fly wheel [9], [10] to account for nonzero rate of angular momentum. Also, the DRS-LIP can be generalized from a constant CoM height (as enforced by assumption (A2)) to a varying height by integrating with the variable-height LIP for stationary surfaces [15].…”

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

“…We compute high-resolution 800 by 800 grids of state-action pairs, as is commonly done for these types of problems [9], [24], [41], [56], [63]. We thus obtain a lookup table of the transition map P(s k , a k ), visualized in the state-action space Q in Fig.…”

Versatile Reactive Bipedal Locomotion Planning Through Hierarchical Optimization

“…2) Constraints: To guarantee the feasibility, we take into account the constraints of ZMP movement (calculated by (14) and (15)), footstep location, CoM vertical motion, upper-body inclination and joint torques. Furthermore, these constraints are expressed in quadratic forms.…”

“…Besides, momentum optimization has attracted more attention in recent years [12], [13]. Zhao et al [14] proposed a hybrid phase-space method to realize dynamic walking on uneven terrain, based on centroidal momentum dynamics. To further enhance the robustness, step location adjustment, angular momentum change and vertical height variation were combined together in a unified MPC framework in [15] and [16], where the fixed height trajectories were used as an inputs.…”