Hierarchical Motion Planning and Control under Unknown Nonlinear Dynamics via Predicted Reachability

2026-03-31

AI Summary

This work proposes a safety-aware and efficient autonomous motion planning and control method for scenarios where the system’s nonlinear dynamics are unknown. The approach employs a hierarchical framework: at the high level, it performs online learning of piecewise affine models through non-uniform adaptive state-space partitioning guided by information-theoretic exploration, and dynamically constructs a weighted directed graph using relaxed reachability conditions to enable path planning; at the low level, affine feedback controllers are synthesized to track the planned trajectories. Key innovations include a predictive reachability analysis tailored for underactuated systems, an efficient state-space partitioning strategy, and formal safety guarantees. Simulations demonstrate that the method effectively balances exploration and exploitation in unknown nonlinear systems while providing rigorous reachability assurances.

Abstract

Autonomous motion planning under unknown nonlinear dynamics requires learning system properties while navigating toward a target. In this work, we develop a hierarchical planning-control framework that enables online motion synthesis with limited prior system knowledge. The state space is partitioned into polytopes and approximates the unknown nonlinear system using a piecewise-affine (PWA) model. The local affine models are identified once the agent enters the corresponding polytopes. To reduce computational complexity, we introduce a non-uniform adaptive state space partition strategy that refines the partition only in task-relevant regions. The resulting PWA system is abstracted into a directed weighted graph, whose edge existence is incrementally verified using reach control theory and predictive reachability conditions. Certified edges are weighted using provable time-to-reach bounds, while uncertain edges are assigned information-theoretic weights to guide exploration. The graph is updated online as new data becomes available, and high-level planning is performed by graph search, while low-level affine feedback controllers are synthesized to execute the plan. Furthermore, the conditions of classical reach control theory are often difficult to satisfy in underactuated settings. We therefore introduce relaxed reachability conditions to extend the framework to such systems. Simulations demonstrate effective exploration-exploitation trade-offs with formal reachability guarantees.

Problem

• motion planning
• unknown nonlinear dynamics
• reachability
• hierarchical control
• autonomous navigation

Innovation

• hierarchical motion planning
• piecewise-affine approximation
• predicted reachability
• adaptive state partitioning
• relaxed reach control