Guiding Collision-Free Humanoid Multi-Contact Locomotion using Convex Kinematic Relaxations and Dynamic Optimization

TL;DR

This work tackles collision-free multi-contact humanoid locomotion in constrained environments by coupling convex, collision-relaxed kinematic planning with a full-body dynamic trajectory optimization. It leverages IRIS-based collision-free regions and Bézier-based trajectory smoothing to produce near-feasible kinematic paths, which then guide a dynamic optimization solved via a nonlinear program with segment-wise discretization and friction-torque constraints. The method is demonstrated on three humanoids (Valkyrie, ergoCub, G1) crossing a knee-knocker door, achieving near-feasible motions within seconds and showing dynamic feasibility in joint space. Limitations include potential self-collisions from convex approximations, seed sensitivity in IRIS, and the absence of explicit balance constraints in the kinematic stage, which the authors propose to address in future work.

Abstract

Humanoid robots rely on multi-contact planners to navigate a diverse set of environments, including those that are unstructured and highly constrained. To synthesize stable multi-contact plans within a reasonable time frame, most planners assume statically stable motions or rely on reduced order models. However, these approaches can also render the problem infeasible in the presence of large obstacles or when operating near kinematic and dynamic limits. To that end, we propose a new multi-contact framework that leverages recent advancements in relaxing collision-free path planning into a convex optimization problem, extending it to be applicable to humanoid multi-contact navigation. Our approach generates near-feasible trajectories used as guides in a dynamic trajectory optimizer, altogether addressing the aforementioned limitations. We evaluate our computational approach showcasing three different-sized humanoid robots traversing a high-raised naval knee-knocker door using our proposed framework in simulation. Our approach can generate motion plans within a few seconds consisting of several multi-contact states, including dynamic feasibility in joint space.

Figures (5)

• Figure 1: Example of a constrained environment requiring dexterous whole-body motions while operating near kinematic limits to traverse it. This highlights both the complexity of of a big humanoid to avoid all obstacles and of a smaller one to pass the high step of the door.
• Figure 2: Block diagram showing a comprehensive overview of our proposed framework. The labels in OCP indicate the equations that describe those optimization problems.
• Figure 3: Procedure followed to construct the safe waypoints, $\xi^{\mathrm{safe}}$ and IRIS sequences, $\{s_{f}\} ~\forall~f \in \mathcal{F}$, from the given fixed, motion, and free frames.
• Figure 4: Side view of left foot IRIS regions, $\mathcal{I}_{\mathrm{LF}, (\cdot)}$, constructed around a rectangular obstacle in between the initial ($x_{(\cdot), 1}$) and final ($x_{(\cdot), 4}$) frame positions. This shows a typical outcome of including the rigid link constraint relaxation to find proxy collision-free motions, resulting in the distance between the LF and LK frames being roughly constant while remaining inside the IRIS regions at the specified times.
• Figure 5: Reachable regions, kinematically feasible trajectories for all robot frames, and dynamically feasible motions of https://carlosiglezb.github.io/humanoids24/valkyrie_door_crossing.html (left), https://carlosiglezb.github.io/humanoids24/ergoCub_door_crossing.html (middle), and https://carlosiglezb.github.io/humanoids24/g1_door_crossing.html (right) as they traverse the knee-knocker door using our framework.