The kinodynamic planning problem is, given a robot system, to find a trajectory from a start state to a goal state, while avoiding obstacles by a safety margin delta (v) and respecting dynamics bounds. Provably good polynomial-time approximation algorithms for optimal kinodynamic planning find trajectories within in of optimal and have a time complexity polynomial in 1/ in and in the geometric complexity of the robot world. The authors obtain such algorithms to find near-optimal trajectories obeying piecewise constant extremal controls and bang-bang control. Previous provably good kinodynamic planning algorithms for robot arms produce nonextremal, and hence locally nonoptimal trajectories. Using parameters in /sub T/ and in /sub S/ and describe closeness to optimality in execution time and observance of the safety margin, the authors derive equicomplexity curves to show how their algorithms permit to tradeoffs between time and safety.
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机译：给定一个机器人系统，鉴于机器人系统，找到从开始状态到目标状态的轨迹，同时避免安全保证金Δ（v）和尊重动态界限的障碍物。 可用于最佳通动力规划的优质多项式近似算法，该近似算法在最佳状态下找到轨迹，在1 / In和机器人世界的几何复杂度中具有时间复杂性多项式。 作者可以获得此类算法，以查找遵守分段恒定极值控制和Bang-Bang控制的近最佳轨迹。 以前可剥夺的机器人武器的良好通动规划算法产生不足，因此局部非优化的轨迹。 使用参数/子T /和/子S / S /和子S / S / S / SIM的参数在执行时间和遵守安全余量中的最优性和遵守安全余量中，导出等式用曲线来展示他们的算法如何允许在时间和安全之间进行权衡。
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