FIRM: Sampling-based feedback motion-planning under motion uncertainty and imperfect measurements

In this paper we present FIRM (Feedback-based Information RoadMap), a multi-query approach for planning under uncertainty, that is a belief-space variant of Probabilistic Roadmap Methods (PRMs). The crucial feature of FIRM is that the costs associated with the edges are independent of each other, and in this sense it is the first method that generates a graph in belief space that preserves the optimal substructure property. From a practical point of view, FIRM is a robust and reliable planning framework. It is robust since the solution is a feedback and there is no need for expensive replanning. It is reliable because accurate collision probabilities can be computed along the edges. In addition, FIRM is a scalable framework, where the complexity of the planning with FIRM is a constant multiplier of the complexity of planning with PRM. In this paper, FIRM is introduced as an abstract framework. As a concrete instantiation of FIRM, we adopt Stationary Linear Quadratic Gaussian (SLQG) controllers as belief stabilizers and introduce the so-called SLQG-FIRM. In SLQG-FIRM we focus on kinematic systems and then extend to dynamical systems by sampling in the equilibrium space. We investigate the performance of SLQG-FIRM in different scenarios.