Abstract
We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion planning, especially those based on discrete abstractions and model predictive control (MPC), suffer from limited scalability with respect to the complexity of the task, the size of the workspace, and the planning horizon. We present a method based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">timed waypoints</i> to address this issue. We show that timed waypoints can help abstract nonlinear behaviors of the system as safety envelopes around the reference path defined by those waypoints. Then the search for waypoints satisfying the STL specifications can be inductively encoded as a mixed-integer linear program. The agents following the synthesized timed waypoints have their tasks automatically allocated, and are guaranteed to satisfy the STL specifications while avoiding collisions. We evaluate the algorithm on a wide variety of benchmarks. Results show that it supports multi-agent planning from complex specification over long planning horizons, and significantly outperforms state-of-the-art abstraction-based and MPC-based motion planning methods. The implementation is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/sundw2014/STLPlanning</uri> .
Highlights
T HE capability of performing automatic task and motion planning according to high-level specifications is what people usually expect from an intelligent and autonomous robotic system
Inspired by the method in [4] where the authors use piece-wise linear (PWL) reference paths and tracking controllers to solve simple reach-avoid synthesis problems, we show that using PWL reference paths one can handle more expressive Signal Temporal Logic (STL) specifications
Empirical results show that our method outperforms other state-of-the-art methods in terms of running time and quality of the planned paths, not to say that our method can handle much more general STL formulas
Summary
T HE capability of performing automatic task and motion planning according to high-level specifications is what people usually expect from an intelligent and autonomous robotic system. MPC-based methods discretize the trajectory with a fixed time step, and the states at each time step are viewed as the decision variables of an optimization problem. These methods have achieved success in a wide range of applications, some obvious disadvantages prevent them from being widely adopted for solving realistic robotic planning problems: To use abstraction-based methods, one needs to construct the bisimilar graph, which heavily relies on domain expertise. We evaluate the proposed method on 8 benchmark synthesis problems with a variety of different scenarios We compare with both abstraction-based and MPC-based methods [5], [6]. The MPC-based method failed in some cases due to the number of decision variables, while our method successfully found a solution
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