Collision detection plays a key role in the simulation of interacting rigid bodies. However, owing to its computational complexity current methods typically prioritize either maximizing processing speed or fidelity to real-world behaviors. Fast real-time detection is achieved by simulating collisions with simple geometric shapes whereas incorporating more realistic geometries with multiple points of contact requires considerable computing power which slows down collision detection. In this work, we present a new approach to modeling and simulating collision-inclusive multibody dynamics by leveraging computer algebra system (CAS). This approach offers flexibility in modeling a diverse set of multibody systems applications ranging from human biomechanics to space manipulators with docking interfaces, since the geometric relationships between points and rigid bodies are handled in a generalizable manner. We also analyze the performance of integrating this symbolic modeling approach with collision detection formulated either as a traditional overlap test or as a convex optimization problem. We compare these two collision detection methods in different scenarios and collision resolution using a penalty-based method to simulate dynamics. This work demonstrates an effective simplification in solving collision dynamics problems using a symbolic approach, especially for the algorithm based on convex optimization, which is simpler to implement and, in complex collision scenarios, faster than the overlap test.

翻译：碰撞检测在刚体相互作用的模拟中起着关键作用。然而，由于计算复杂性，当前方法通常优先考虑最大化处理速度或对真实世界行为的保真度。通过用简单几何形状模拟碰撞可实现快速实时检测，而引入更具真实性的多接触点几何形状则需要大量计算能力，从而减慢碰撞检测速度。本研究提出一种利用计算机代数系统（CAS）对包含碰撞的多体动力学进行建模和模拟的新方法。该方法以通用方式处理点与刚体之间的几何关系，从而能够灵活建模从人体生物力学到带对接接口的空间机械臂等多种多体系统应用。我们还分析了将这种符号建模方法与碰撞检测（可采用传统重叠测试或凸优化问题形式）相结合的集成性能。我们比较了这两种碰撞检测方法在不同场景下的表现，并采用基于罚函数的方法模拟动力学以解决碰撞问题。本研究展示了利用符号方法有效简化碰撞动力学问题求解的过程，尤其是基于凸优化的算法更易实现，且在复杂碰撞场景中比重叠测试更快。