Trusted Polytopic Action Sets for Fast Planning in Underactuated Systems

Abstract:Underactuated systems pose a challenge for convex motion planning because their dynamically feasible motions lie on a manifold of trajectories in function space. Building on our earlier formulation of polytopic action sets (PAS), this paper presents a method for rapidly generating, online, trusted convex sets of short-horizon actions for underactuated and potentially nonlinear systems. Around a nominal trajectory, we construct local finite-dimensional action coordinates in which each parameter vector encodes a complete nearby motion through an affine trajectory map, rendering collision-avoidance and control bounds linear. To remain consistent with the nonlinear dynamics, we introduce a dynamics-violation metric and extract a trusted convex inner approximation using an IRIS-inspired inflation procedure directly in action space. The resulting PAS are reusable convex families of actions that can be queried and composed with linear programs, and a PAS-guided tree expansion treats nodes as composed reachable families rather than single trajectories, coupling local nonlinear fidelity with convex reuse for longer-horizon planning. The planner solves cluttered planar scenes in tens of milliseconds (14-78x faster than a kinodynamic RRT baseline) and reduces terminal error on a nonlinear underactuated benchmark by 26-86% over sampling and NLP baselines.

Accepted for publication in IEEE Control Systems Letters (L-CSS); to be presented at the 2026 IEEE Conference on Decision and Control. Code available at this https URL

Systems and Control (eess.SY); Robotics (cs.RO)

arXiv:2608.24019 [eess.SY]

(or arXiv:2608.24019v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2608.24019 arXiv-issued DOI via DataCite (pending registration)

IEEE Control Systems Letters, vol. 10, pp. 2173-2178, 2026

https://doi.org/10.1109/LCSYS.2026.3718036 DOI(s) linking to related resources