Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms that can be built on top of collision detection. In this work, we propose a set of differentiable collision detection algorithms between capsules and padded polygons by formulating these problems as differentiable convex quadratic programs. The resulting algorithms are able to return a proximity value indicating if a collision has taken place, as well as the closest points between objects, all of which are differentiable. As a result, they can be used reliably within other gradient-based optimization methods, including trajectory optimization, state estimation, and reinforcement learning methods.
翻译:碰撞探测在模拟、控制和机器人系统的学习中起着重要作用。 但是,在物体的配置方面,没有任何现有方法可以区别,大大限制了在碰撞探测后可以建立的算法类型。在这项工作中,我们提出了一系列在胶囊和加加多边形之间可以区别的碰撞探测算法,将这些问题作为不同的锥形二次方程式来表述。由此产生的算法能够返回近距离值,表明是否发生了碰撞,以及物体之间最接近的点,所有这些点都是可以区别的。因此,这些算法可以在其他梯度优化方法中可靠地使用,包括轨道优化、状态估计和强化学习方法。