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arXiv 2203.15977eess.SYcs.ROcs.SY
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基于最优化的高效避碰算法的Minkowski和逼近

Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance

Johns Hopkins University(约翰斯·霍普金斯大学)

James Guthrie, Marin Kobilarov, Enrique Mallada

摘要:

基于非线性规划的自主系统的运动规划方法在结合各种动力学、目标和约束方面提供了极大的灵活性。这种工具的一个限制是难以有效地表示非平凡形状的避障条件。例如,可以定义适合于在N个时间步长内围绕M个凸多面体导航的圆形机器人的规范设置中的非线性规划求解器的碰撞避免约束。然而,它需要引入(2+L)MN个额外的约束和LMN个额外的变量,其中L是每个多面体的半平面的数量,导致更大的非线性程序,求解时间更慢且更不可靠。在本文中,我们克服了这个问题,通过建立封闭形式的表示的避碰条件外近似的Minkowski和条件的碰撞。我们的解决方案只需要MN约束(没有额外的变量),导致一个较小的非线性规划。在杂乱环境中自动驾驶汽车和四轴飞行器的运动规划问题上,我们分别实现了4.8倍和8.7倍的加速比,求解时间的方差显著减少,并且使用外近似对性能的影响可以忽略不计。

英文摘要:

Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming solvers in the canonical setting of a circular robot navigating around M convex polytopes over N time steps. However, it requires introducing (2+L)MN additional constraints and LMN additional variables, with L being the number of halfplanes per polytope, leading to larger nonlinear programs with slower and less reliable solving time. In this paper, we overcome this issue by building closed-form representations of the collision avoidance conditions by outer-approximating the Minkowski sum conditions for collision. Our solution requires only MN constraints (and no additional variables), leading to a smaller nonlinear program. On motion planning problems for an autonomous car and quadcopter in cluttered environments, we achieve speedups of 4.8x and 8.7x respectively with significantly less variance in solve times and negligible impact on performance arising from the use of outer approximations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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