Whole-body MPC and sensitivity analysis of a real time foot step sequencer for a biped robot Bolt

TL;DR

This work tackles robust bipedal locomotion by fusing a whole-body Model Predictive Controller with a real-time footstep sequencer capable of emergent stepping at 100 Hz. The approach relies on a fixed-horizon WB-MPC and a sensitivity analysis of the sequencer to disturbances in the Divergent Component of Motion ($DCM$), facilitated by Fiacco's framework. In simulation, Bolt demonstrates velocity tracking, perturbation rejection, and navigation on cluttered terrain, with footstep adaptation arising naturally from the optimization rather than precomputed trajectories. The study highlights the practicality of unified WB planning for unstable humanoids and lays groundwork for hardware validation and extended sensitivity analysis to enhance robustness guarantees.

Abstract

This paper presents a novel controller for the bipedal robot Bolt. Our approach leverages a whole-body model predictive controller in conjunction with a footstep sequencer to achieve robust locomotion. Simulation results demonstrate effective velocity tracking as well as push and slippage recovery abilities. In addition to that, we provide a theoretical sensitivity analysis of the footstep sequencing problem to enhance the understanding of the results.

Figures (8)

• Figure 1: Bipedal robot bolt walking in PyBullet using whole-body MPC on cluttered terrain.
• Figure 2: Solution space example of $p_{T,y}$ (left) and $b_{T,y}$ (right) as a function of the DCM disturbance $\theta \sim \mathcal{N}(0, 0.005)$ generated with 1000 samples. The optimal solution is represented in red, and no inequality constraints is active.
• Figure 3: Position of the feet and DCM in the Cartesian plane along a generated step sequence. The walking sequence was generated with $H_u=3\;s$ using the input parameters from Table \ref{['tab:QP-params']}. The imposed speed is $V_x^*=\frac{l_{\text{nom}}}{T_{\text{nom}}}=0.33m.s^{-1}$. All constraints are satisfied, and the nominal speed is achieved.
• Figure 4: Simplified architecture of Bolt's walking controller.
• Figure 5: Comparison of the CoM (purple), the DCM (green), and the foot positions (red for left, blue for right) along the $y$-axis over time during walking at $V^*_x = 0.33 \, {m.s^{-1}}$. Top: Unperturbed walking. Bottom: Walking perturbed at $t = 5 \, \text{s}$ by an applied force of $F = 6.3 \, \text{N}$ along the $y$-axis at the robot's base for 0.1 s.