Mathematical modeling of a robot collision with its environment

Abstract In this article the collision of a robot with its environment is studied. In normal applications of a robot arm, a collision takes place because of the velocity of the end effector relative to the object at the time of contract. The collision has effects on the velocities and internal forces of the robotic system. Firstly, the generalized velocities representing joint rates have abrupt changes at the moment of collison with the environment. The mathematical model is derived to establish the quantitative relationship between this abrupt change and the severity of the collision. The latter is represented by either an external impulsive force or the instantaneous change of the linear velocity of the contact point. Secondly, internal to the system, large impulsive forces and torques of constraint may develop at each joint because of the collision. These impulses cause possible damages to the system. The mathematical model is also derived to establish a quantitative relation between the impulsive forces and torquest of constraint and the collision. These two models are applied to a Stanford Arm designed to pick up an object by its end effector, and the consequences of the collision are analyzed.