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This paper introduces a method for generating trusted polytopic action sets (PAS) that enables rapid motion planning for underactuated systems by constructing local finite-dimensional action coordinates around nominal trajectories. By employing a dynamics-violation metric and an IRIS-inspired inflation procedure, the authors create reusable convex families of actions that facilitate efficient planning while maintaining nonlinear fidelity. The proposed approach significantly outperforms traditional kinodynamic RRT methods, achieving planning speeds 14–78 times faster and reducing terminal error by 26–86% on benchmark tasks.
Trusted polytopic action sets enable motion planning for underactuated systems at unprecedented speeds, achieving up to 78 times faster planning than conventional methods.
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 letter 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– $78\times $ faster than a kinodynamic RRT baseline) and reduces terminal error on a nonlinear underactuated benchmark by 26–86% over sampling and NLP baselines.
