用非线性规划法生长位形空间中的凸无碰撞区域
Growing Convex Collision-Free Regions in Configuration Space using Nonlinear Programming
摘要：
配置空间中的运动规划的最困难部分之一是确保轨迹不会与环境中的任务空间障碍物碰撞。在配置空间中生成凸的且无碰撞的区域可以将碰撞检查的计算负担与运动规划分离。为此，我们提出了对IRIS（半定规划迭代区域膨胀）[5]的扩展，允许它在配置空间中操作。我们的算法IRIS-NP（半定和非线性规划的迭代区域膨胀）使用非线性优化来添加分离的超平面，从而支持更一般的非线性约束。IRIS-NP与Amice等人[1]并行开发，IRIS-NP将严格的区域无冲突认证与概率认证相交换，并在配置空间坐标中更快地生成区域。IRIS-NP还为C-IRIS提供了可靠的初始化，以减少认证所需的迭代次数。我们证明了IRIS-NP可以扩展到双臂机械手，并可以使用相同的机械处理额外的非线性约束。最后，我们展示了我们实现的元素的消融，以证明它们的重要性。
英文摘要：
One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free in configuration space can separate the computational burden of collision checking from motion planning. To that end, we propose an extension to IRIS (Iterative Regional Inflation by Semidefinite programming) [5] that allows it to operate in configuration space. Our algorithm, IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming), uses nonlinear optimization to add the separating hyperplanes, enabling support for more general nonlinear constraints. Developed in parallel to Amice et al. [1], IRIS-NP trades rigorous certification that regions are collision free for probabilistic certification and the benefit of faster region generation in the configuration-space coordinates. IRIS-NP also provides a solid initialization to C-IRIS to reduce the number of iterations required for certification. We demonstrate that IRIS-NP can scale to a dual-arm manipulator and can handle additional nonlinear constraints using the same machinery. Finally, we show ablations of elements of our implementation to demonstrate their importance.
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