On the transition phase in robotics: impact models, dynamics and control

The aim of this note is threefold: i) to introduce a rigorous mathematical model of impulsive collisions dynamics through the use of Schwartz´s distributions; ii) to study the relationships between impulsive and continuous dynamics models of impacts (i.e. models composed of mass, spring, damper); and iii) to analyze the difficulties associated with the transition phase control. The authors start a tentative comparison on two models of impacts through a simple example of a mass colliding with a wall. Numerical simulations illustrating the examples are presented