Contact Transition Modelling on Planar Manipulation System with LuGre Friction Model

In this paper, for motion planning and controlling on manipulation system, a novel contact transition model is proposed by employing the LuGre friction model instead of Coulomb friction. The LuGre model is a differential equation with a state variable defined as the microscopic average bristle deflection between bodies and has the capability of more realistic friction properties. The stick-slip transition in the tangential directions at contact points is firstly formulated as a continuous system because the LuGre model is continuous at zero tangential contact velocities. The impact transition is secondly formulated by describing the dynamics of collided bodies during the impact as differential equations with respect to the normal impulse instead of time. Here, the LuGre model is modified to the differential one with respect to the normal impulse, where the state variable can be interpreted as the stored energy of the bristle deflection. Numerical simulations are performed to show the effectiveness of the formulations.