A receding-horizon multi-contact motion planner for legged robots in challenging environments

We present a novel receding-horizon multi-contact motion planner for legged robots in challenging scenarios, able to plan motions such as chimney climbing, navigating very narrow passages or crossing large gaps. Our approach adds new capabilities to the state of the art, including the ability to reactively re-plan in response to new information, and planning contact locations and whole-body trajectories simultaneously, simplifying the implementation and removing the need for post-processing or complex multi-stage approaches. Our method is more resistant to local minima problems than other potential field based approaches, and our quadratic-program-based posture generator returns nodes more quickly than those of existing algorithms. Rigorous statistical analysis shows that, with short planning horizons (e.g., one step ahead), our planner is faster than the state-of-the-art across all scenarios tested (between 45% and 98% faster on average, depending on the scenario), while planning less efficient motions (requiring 5% fewer to 700% more stance changes on average). In all but one scenario (Chimney Walking), longer planning horizons (e.g., four steps ahead) extended the average planning times (between 73% faster and 400% slower than the state-of-the-art) but resulted in higher quality motion plans (between 8% more and 47% fewer stance changes than the state-of-the-art).

💡 Research Summary

The paper introduces a receding‑horizon multi‑contact motion planner designed for legged robots operating in highly constrained and unstructured environments such as chimney climbing, narrow passages, and large gaps. Unlike traditional Contact‑Before‑Motion (CBM) or Motion‑Before‑Contact (MBC) approaches that separate contact selection from whole‑body trajectory generation, the proposed framework simultaneously determines contact locations and whole‑body motions within a single planning loop.

The core of the method is a breadth‑first tree search that expands nodes up to a user‑defined horizon depth κ_max. At each expansion, a posture generator based on Vector‑Field Inequalities (VFI) and quadratic programming (QP) checks whether a kinematically feasible whole‑body trajectory exists between the current stance and a candidate next stance. By embedding this feasibility check directly into the tree expansion, the planner avoids generating unreachable stance sequences—a limitation of earlier multi‑stage pipelines such as CVBFP.

Vector‑Field Inequalities transform nonlinear geometric constraints (collision avoidance, balance, joint limits, etc.) into linear constraints on the joint velocity vector ˙q. These linear constraints are incorporated into a QP that minimizes a task‑space error while respecting the VFI‑derived bounds. The robot’s pose and motion are represented using dual quaternion algebra, which provides a compact and numerically stable description of rotations and translations, facilitating the formulation of the QP.

The planner offers two main operating regimes. With a short horizon (one step ahead), the tree remains shallow, and the QP solves in a few milliseconds, yielding planning times 45 %–98 % faster than the state‑of‑the‑art Contact‑Very‑Best‑First‑Planning (CVBFP) across all test scenarios. However, the resulting motions may involve more stance changes (up to 700 % more) because the planner optimizes locally. With a longer horizon (four steps ahead), the planner explores a richer set of stance sequences, leading to 8 %–47 % fewer stance changes and higher overall motion quality, at the cost of increased computation time (ranging from 73 % faster to 400 % slower than CVBFP depending on the scenario). The only exception is the Chimney Walking scenario, where longer horizons degrade planning speed without a clear quality benefit.

Experimental validation is performed on the Corin hexapod robot in four challenging scenarios. For each scenario, 30 randomized trials are executed, and Bayesian statistical analysis is used to compare planning time, number of stance changes, and success rate against CVBFP. Results confirm the claimed speed‑quality trade‑offs and demonstrate the planner’s ability to re‑plan rapidly when new information (e.g., updated terrain perception) becomes available.

Additional contributions include a numerical integration scheme with contact‑drift correction to maintain contact consistency during posture generation, and a systematic analysis of local‑minimum problems that plague potential‑field‑based planners. By integrating VFI constraints directly into the QP, the proposed method mitigates these minima and provides a more robust search landscape.

Overall, the work advances the state of legged‑robot motion planning by delivering a unified, receding‑horizon framework that simultaneously handles contact selection and whole‑body trajectory synthesis, offers tunable performance‑quality trade‑offs via the horizon depth, and demonstrates statistically significant improvements over existing methods. Future directions suggested by the authors include extending the approach to dynamic obstacles, incorporating learning‑based heuristics for faster tree expansion, and real‑time hardware deployment on a broader class of legged platforms.