In this work, we present a novel, reactive, modulated control strategy based on dynamical systems (DS) for planning in the context of multiple nonconvex obstacles. Our DS modulation strategy leverages an on-manifold planning methodology and provides several methods for real-time on-manifold navigation around nonconvex obstacles. We introduce a sample-based obstacle representation for complex, nonconvex obstacles, as well as a projection-based method for representing surfaces, such as tables, cylinders, and ellipsoids. These representations can be combined to represent multiple obstacles and obstacle types (sample- or projection-based) with a single, continuously differentiable function. We validate our approach in several real-world scenarios, including navigation within (simulated) constrained environments, as well as reactive control of a real 7-DoF manipulator with dynamic obstacles (including humans) while utilizing a 1 kHz control loop rate. Using our sample-based representation, we can calculate the obstacle representation function in less than 1 ms with up to 35 k points using a CPU implementation, and up to 600 k points with a GPU implementation.

中文翻译：

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非凸障碍反应动态系统调制的流形策略

在这项工作中，我们提出了一种基于动力系统（DS）的新型反应式调制控制策略，用于在多个非凸障碍物的背景下进行规划。我们的 DS 调制策略利用流形上规划方法，并提供多种方法来围绕非凸障碍物进行实时流形导航。我们引入了用于复杂非凸障碍物的基于样本的障碍物表示，以及用于表示表面（例如桌子、圆柱体和椭球体）的基于投影的方法。这些表示可以组合起来，用单个连续可微函数来表示多个障碍物和障碍物类型（基于样本或基于投影）。我们在几个现实场景中验证了我们的方法，包括（模拟）受限环境中的导航，以及在利用 1 kHz 控制循环速率时对具有动态障碍物（包括人类）的真实 7-DoF 机械臂进行反应控制。使用基于样本的表示，我们可以在不到 1 毫秒的时间内计算出障碍物表示函数，使用 CPU 实现时最多可计算 35 k 点，使用 GPU 实现时可计算最多 600 k 点。