Dynamic modeling and simulation of the multi-point collision and contact problem of multi-legged robots

The problem of multi-point collision and contact in multi-legged robots involves complex dynamics with multiple closed loops, variable topology, and numerous contact points, making simulations challenging. Additionally, Zeno behavior—characterized by an infinite number of discrete transitions within a finite time—is likely to occur, reducing computational efficiency and potentially causing simulations to stall. This paper establishes a linear complementary dynamic model to study the collision and contact problem of multi-legged mobile robots. For the uncertainty of multi-point collision and contact, we use sets and transformation matrices to represent the number and position changes of the points that collide or contact with the ground. This paper separately studies the problems of multi-point collision and multi-point continuous contact and considers the coupling effect of collision and continuous contact. A new criterion to determine the state of continuous contact is proposed, and modifications are made to the relevant linear complementary equations to prevent the Zeno behavior. Finally, several numerical examples are provided to verify the effectiveness of the method.