Collision detection is one of the cores in robotics and one of the keys to ensuring the safe operation of robots. How to accurately and efficiently obtain the contact state and shortest distance between two objects has always been a popular issue. Collision detection is widely used in fields such as physical simulation and robot motion planning. For example, when planning a robot's motion path, it is often necessary to fully consider collision issues between the robot and its surrounding environment as well as its own components, in order to obtain a safe and feasible optimal path.

Collision Detection based on Closed-form Contact Space

CFC algorithm

This project investigates collision detection between two bodies based on closed-form contact space parameterization. It starts from two ellipsoids, then generalized to two convex bodies with smooth boundaries. Using nonlinear optimization techniques, the distance between the contact space and the center of one body are computed. Then, the proximity distance or penetration depth can be derived. The proposed framework is able to deal with: (1) the static case where the contact status, separation distance or penetration depth and the corresponding witness points are resulted; and (2) the continuous case where the first time-of-impact or the minimum separation distance are computed.

GPD-CFC algorithm

This project firstly proposes GPDMink, a method to compute closed-form Minkowski sums between two objects, one of which has nonlinear deformations (e.g. tapering). Based on this, GPD-CFC algorithm is developed, which obtains the contact status, proximity distance/penetration depth, contact normals, etc. This work is published in 2025 in the journal of Multibody System Dynamics.

【Paper】

[1] Ruan, S.* and Mei, J.,2025. Gradient-parameterized deformable Minkowski sum with applications on contact detection. Multibody System Dynamics, 1-26.

https://link.springer.com/article/10.1007/s11044-025-10134-5

[2] Ruan, S., Wang, X. and Chirikjian, G.S., 2022. Collision Detection for Unions of Convex Bodies with Smooth Boundaries using Closed-form Contact Space Parameterization. IEEE Robotics and Automation Letters, 7(4), pp.9485-9492

https://ieeexplore.ieee.org/document/9829274

Collision Probability

Compared to the traditional deterministic collision detection, this work aims to compute the probability of collisions when the object poses are uncertain. Since there is no closed-form solution, the algorithm computes an upper bound of the collision probability. Then, based on the probability information, the robot is guided to avoid contacts with obstacles in the uncertain environments. The method is published in 2025 in the journal of IEEE Robotics and Automation Letters (RA-L).

【Paper】

[1]  Wang, X., Ruan, S., Meng, X. and Chirikjian, G.S., 2025. Enhanced Probabilistic Collision Detection for Motion Planning Under Sensing Uncertainty. IEEE Robotics and Automation Letters, 10(10), pp.10910 - 10917

https://ieeexplore.ieee.org/document/11145942