Abstract:

We propose an implicit, event-driven, penalty-based method for modeling rigid body contact and collision that is useful for design and analysis of control algorithms for precision robotic assembly tasks. The method is based on Baumgarte’s method of differential algebraic equation index reduction in which we modify the conventional constraint stabilization to model object collision, define a finite state machine to model transition between contact and non-contact states, and represent the robot and task object dynamics as a single set of differential algebraic inequalities. The method, which is realized natively in Modelica, has some advantages over conventional penalty-based methods: The resulting system is not numerically stiff after the collision transient, it enforces constraints for object penetration, and it allows for dynamic analysis of the Modelica model beyond time-domain simulation. We provide three examples: A bouncing ball, a ball maze, and a delta robot controlled to achieve soft collision and maintain soft contact with an object in its environment.