Robotic Manipulator Collisions: Modeling and Simulation

In this paper, a new formulation of the dynamics of a robotic manipulator work environment is presented. The work environment is modeled in a way that permits the robot transition to and from contact with the work environment to be effectively simulated. This method circumvents the discontinuities inherent in previously proposed models of work environment dynamic models that have, until now, prevented researchers from considering that phase of manipulation. Combined with an existing model of the manipulator dynamics, the overall model of the manipulator-work environment system is such that the system states evolve continuously in time, as is the case in reality. Specifically, a continuous dynamics model is presented which models dynamic behavior of an n degree of freedom rigid link robotic manipulator during the transition to and from frictionless point contact with a work environment. The dynamic model of the work environment is sufficiently general to encompass, as limiting cases, both constrained motion and compliant motion contacts. The general properties of the work environment dynamics model are readily altered with only two parameters. A singular perturbation analysis provides an analytical approach to verification of the properties of the model of the work environment known to be true from an intuitive perspective. Results concerning the behavior of the impact force during a collision between the manipulator and work environment are also obtained using a singular perturbation theory approach. Detailed dynamic simulation results are given to illustrate the behavior of the proposed model. Simulation results of a two-degree-of-freedom manipulator with proportional and derivative control applied during the transition from noncontact to contact motion are given. Comparison of simulation results to experimentally obtained results reported in the robotics literature reveal a remarkable similarity in the time responses, given the simplicity of the work environment dynamic model.