Extended Jacobian for Redundant Robots Obtained from the Kinematics Constraints

Abstract. This paper presents a proposal for a new extended Jacobian method based on kinematic constraints, exploring only singularities of the kinematic chain. It is presented the development of the new extended Jacobian as well as their properties. These method can be applied to analyze the behavior of redundant robots on perfoming a task. Redundant robots are used to perform tasks which require some type of extra mobility, for example when it is necessary to avoid obstacles inside their workspace. In general the kinematic redundancy condition does not allow to find the solutions the solution of inverse kinematics directly. Methods based on pseudoinverse matrix and extended Jacobian are generally useful for solving inverse kinematics for redundant robots. However, these methods have limitations like metric problems and algorithmic singularities that do not belong to the kinematic chain. These limitations decrease the robot’s ability to perform movements, while away from their kinematic singularities. Based on screw theory, the method of kinematic constraints consists in add Assur virtual chains to perform tasks that retricts movements, such as trajectory generation, collision avoidance, among others. To validate the proposal an example for redundant robot P3R is developed.