Efficient Motion Planning With Minimax Objectives: Synergizing Interval Prediction and Tree-Based Planning

This paper presents an efficient motion planning framework for a perturbed linear system using a minimax objective function while ensuring the safety of the system. Specifically, the proposed approach is naturally deployed to handle model uncertainties by a recursive least squares-based set-membership mechanism. Next, a minimax-based objective optimization problem is formed to handle the goal flexibility. The robust model predictive control algorithm is then designed to solve this robust optimization objective. Furthermore, a refined strategy is able to approximate robust objectives by synergizing interval prediction and tree-based planning to achieve the best surrogate performance. It is extended to incorporate a hierarchical control architecture in a specific context. This extension serves to enhance path efficiency and, in turn, alleviates the constraints associated with modeling assumptions. The primary difficulty involves integrating and adjusting theoretical assurances at each level, a task accomplished through a comprehensive examination of suboptimality from end to end. The proposed framework is versatile across a variety of models, incorporating a solid, data-informed approach for selecting models. This integration permits a more flexible approach to modeling assumptions. Moreover, we consistently maintain the practicability of our method throughout its application, a fact that is evidenced by its successful deployment in complex simulated settings.