Sampling-based motion planning with temporal goals

Abstract

Abstract-This paper presents a geometry-based, multilayered synergistic approach to solve motion planning problems for mobile robots involving temporal goals. The temporal goals are described over subsets of the workspace (called propositions) using temporal logic. A multi-layered synergistic framework has been proposed recently for solving planning problems involving significant discrete structure. In this framework, a high-level planner uses a discrete abstraction of the system and the exploration information to suggest feasible high-level plans. A low-level sampling-based planner uses the physical model of the system, and the suggested high-level plans, to explore the state-space for feasible solutions. In this paper, we advocate the use of geometry within the above framework to solve motion planning problems involving temporal goals. We present a technique to construct the discrete abstraction using the geometry of the obstacles and the propositions defined over the workspace. Furthermore, we show through experiments that the use of geometry results in significant computational speedups compared to previous work. Traces corresponding to trajectories of the system are defined employing the sampling interval used by the low-level algorithm. The applicability of the approach is shown for second-order nonlinear robot models in challenging workspace environments with obstacles, and for a variety of temporal logic specifications. I. INTRODUCTIONTraditional motion planning algorithms have considered the problem of constructing a motion plan for a given robot model, such that the plan takes the robot from a set of initial states to a set of goal states while avoiding obstacles in the workspace [1], [2]. A class of planning approaches have been proposed recently that use a richer framework to specify complex temporal goals like coverage, ordering of events, etc [3]-[8] using formalisms like Linear Temporal Logic (LTL) (cf. [9]). As an example, the temporal goal "Eventually visit region A followed by a visit to region B or region C", can be easily expressed using LTL. An approach for motion planning with deterministic µ-calculus specifications has been proposed recently in [10].To deal with LTL constraints, a hierarchical approach for motion planning for point-mass linear robot models with temporal goals has been proposed recently in [7]. The focus of the approach is on the construction of provably correct motion plans. Currently, the approach can handle secondorder linear robot models and more work needs to be done to extend the approach for nonlinear robot models. An approach combing synthesis technique with receding horizon control has also been proposed recently for linear robot models [8].The focus of this paper is motion planning problems involving, nonlinear robot models with finite geometry, com-

Receding Horizon Control in Dynamic Environments from Temporal Logic Specifications

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