Sampling-based approximate optimal temporal logic planning. Li, L. & Fu, J. In Proceedings - IEEE International Conference on Robotics and Automation, pages 1328-1335, 5, 2017. IEEE. ![Sampling-based approximate optimal temporal logic planning [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
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Website abstract bibtex In this paper, we propose a sampling-based policy iteration for optimal planning under temporal logic constraints. The method integrates approximate optimal control, impor-tance sampling, and formal methods. For a subclass of linear temporal logic, the planning problem is transformed to an optimal control problem for a hybrid system where discrete transitions are triggered by linear time events in temporal logic. Instead of solving the Hamilton-Jacobi-Bellman equation, we use policy function approximation to reduce the problem into a search of an optimal weight vector that parametrizes the near-optimal policy for given bases. Then, we incorporate Model Reference Adaptive Search — an importance sampling-based optimization algorithm to perform a sample-efficient search within the parameter space of policy function approximations. Facing the discontinuity in cost function introduced by temporal logic constraints and system dynamics, we introduce 1) a rank function in formal logic specifications to enable sample-efficient search; 2) specification-guided basis selection. Under mild technical assumptions, the proposed algorithm converges, with probability one, to a global approximate optimal policy that ensures the satisfaction of temporal logic constraints. The correctness and efficiency of the method are demonstrated through numerical experiments including temporal logic plan-ning for a linear system and a nonlinear mobile robot.
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abstract = {In this paper, we propose a sampling-based policy iteration for optimal planning under temporal logic constraints. The method integrates approximate optimal control, impor-tance sampling, and formal methods. For a subclass of linear temporal logic, the planning problem is transformed to an optimal control problem for a hybrid system where discrete transitions are triggered by linear time events in temporal logic. Instead of solving the Hamilton-Jacobi-Bellman equation, we use policy function approximation to reduce the problem into a search of an optimal weight vector that parametrizes the near-optimal policy for given bases. Then, we incorporate Model Reference Adaptive Search — an importance sampling-based optimization algorithm to perform a sample-efficient search within the parameter space of policy function approximations. Facing the discontinuity in cost function introduced by temporal logic constraints and system dynamics, we introduce 1) a rank function in formal logic specifications to enable sample-efficient search; 2) specification-guided basis selection. Under mild technical assumptions, the proposed algorithm converges, with probability one, to a global approximate optimal policy that ensures the satisfaction of temporal logic constraints. The correctness and efficiency of the method are demonstrated through numerical experiments including temporal logic plan-ning for a linear system and a nonlinear mobile robot.},
bibtype = {inProceedings},
author = {Li, Lening and Fu, Jie},
booktitle = {Proceedings - IEEE International Conference on Robotics and Automation}
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