Robust Planning and Control For Polygonal Environments via Linear Programming
Robust Planning and Control For Polygonal Environments via Linear Programming
复制标题
通过线性规划对多边形环境进行鲁棒规划和控制
DOI：
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发表时间：
2019
期刊：
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通讯作者：
Roberto Tron
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作者：
Mahroo Bahreinian;Erfan Aasi;Roberto Tron
在本文中，我们关注通过线性规划对多边形环境进行单元分解的一组控制器的设计。我们提出的方法的核心由凸最小-最大公式组成，该公式基于相对于一组地标的相对位移测量来合成输出反馈控制器。使用分段线性控制李亚普诺夫函数和控制屏障函数约束来制定优化问题，以提供稳定性和安全性的保证。内部最大化问题确保每个单元中的所有点都满足这些约束，而外部最小化问题平衡不同的约束以优化鲁棒性。我们通过形成内部最大化问题的对偶，将这个最小-最大优化问题转换为常规线性规划问题。虽然原则上我们的方法适用于任何具有分段线性动力学的系统，但在本文中作为概念证明，我们将其应用于一阶和二阶积分器。我们通过模拟表明，所得到的控制器对于环境的显着变形具有鲁棒性。
In this paper, we are concerned with the design of a set of controllers, on a cell decomposition of a polygonal environment through Linear Programming. The core of our proposed method consists of a convex min-max formulation that synthesizes an output-feedback controller, based on relative displacement measurements with respect to a set of landmarks. The optimization problem is formulated using piece-wise linear Control Lyapunov Function and Control Barrier Function constraints, to provide guarantees of stability and safety. The inner maximization problem ensures that these constraints are met by all the points in each cell, while the outer minimization problem balances the different constraints to optimize robustness. We convert this min-max optimization problem to a regular Linear Programming problem, by forming the dual of the inner maximization problem. Although in principle our approach is applicable to any system with piecewise linear dynamics, in this paper as a proof of concept, we apply it to first and second order integrators. We show through simulations that the resulting controllers are robust to significant deformations of the environment.