We present a semi-infinite program (SIP) solver for trajectory optimizations of general articulated robots. These problems are more challenging than standard nonlinear program by involving an infinite number of nonconvex, collision constraints. Prior SIP solvers based on constraint sampling cannot guarantee the satisfaction of all constraints. Instead, our method uses a conservative bound on articulated body motions to ensure the solution feasibility throughout the optimization procedure. We further use subdivision to adaptively reduce the error in conservative motion estimation. Combined, we prove that our SIP solver guarantees feasibility while approaching the optimal solution of SIP problems up to arbitrary user-provided precision. We demonstrate our method toward several trajectory optimization problems in simulation, including industrial robot arms and UAVs. The results demonstrate that our approach generates collision-free locally optimal trajectories within a couple of minutes.

中文翻译：

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通过细分在碰撞约束下证明可行的半无限程序

我们提出了一种用于通用关节机器人轨迹优化的半无限程序（SIP）求解器。这些问题比标准非线性程序更具挑战性，因为它们涉及无限数量的非凸碰撞约束。现有的基于约束采样的SIP求解器不能保证满足所有约束。相反，我们的方法使用关节体运动的保守界限来确保整个优化过程中解决方案的可行性。我们进一步使用细分来自适应地减少保守运动估计中的误差。结合起来，我们证明了我们的 SIP 求解器保证了可行性，同时接近 SIP 问题的最优解，达到任意用户提供的精度。我们在模拟中展示了我们针对几个轨迹优化问题的方法，包括工业机器人手臂和无人机。结果表明，我们的方法可以在几分钟内生成无碰撞的局部最优轨迹。