Trusted Polytopic Action Sets for Fast Planning in Underactuated Systems

• URL: http://arxiv.org/abs/2608.24019v1
• Date: Tue, 25 Aug 2026 03:18:32 GMT
• Title: Trusted Polytopic Action Sets for Fast Planning in Underactuated Systems
• Abstract summary: Underactuated systems pose a challenge for convex motion planning because their motions lie on a manifold of trajectories in function space.<n>This paper presents a method for rapidly generating, online, trusted convex sets of short-horizon actions for underactuated and potentially nonlinear systems.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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