Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging non-convex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a Linear Program. This reformulation enables us to address motion planning as a Mixed Integer Linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum within approximately 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

翻译：长时域、动态可行的机器人运动规划中的优化方法需要处理极具挑战性的非凸和不连续优化问题。传统方法常因这些问题的非线性特性而失效。我们提出一种利用系统学习表示（即多面体动作集）的技术，以高效计算长时域轨迹。通过采用适当的多面体动作集序列，我们将长时域动态可行运动规划问题转化为线性规划问题。这一转化使我们能够将运动规划作为混合整数线性规划（MILP）求解。我们通过为力矩受限摆锤在大约0.75毫秒内识别摆起运动，展示了多面体动作集与运动规划（PAAMP）方法的有效性。该方法特别适用于解决腿式机器人和空中机器人等动态欠驱动系统中的复杂运动规划与长时域约束满足问题（CSPs）。