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This paper introduces a hierarchical motion planning and control framework for autonomous navigation under unknown nonlinear dynamics, using a piecewise-affine (PWA) approximation of the system learned online. The framework employs a non-uniform adaptive state space partition strategy to refine the partition only in task-relevant regions, reducing computational complexity. By abstracting the PWA system into a directed weighted graph with edges verified using reach control theory and predictive reachability, the method achieves effective exploration-exploitation trade-offs with formal reachability guarantees, even extending to underactuated systems via relaxed reachability conditions.
Overcome the curse of dimensionality in motion planning for unknown dynamics by adaptively refining state-space partitions only where needed, enabling efficient online learning and control.
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.
