Cartesian Sliding PID Control Under Jacobian Uncertainty of Robotics Hands: Executing Transition Tasks

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The necessity to make complex tasks have increased in many robotics systems such as cooperatives robots or robotics hands. When each robot execute free and constrained motion tasks involves change into dynamics for rigid contact. At the time of impact regime the derivative of the velocity vector is not well-defined, therefore it is difficult to design controller for transition task. The trivial approach to avoid the impact is presented commuting consistently ODE- and DAE-based controller to insure formally zero contact velocity, -at any given arbitrarily time and for any initial condition. One way to circumvent this, it is to know exactly the commuting time to guarantee zero contact velocity such that impulsive dynamics will not arise and stable transition can be obtained. The novelty of our approach is characterized in the fact that very fast decentralized cartesian cooperative tracking is obtained without using the model of the robot nor exact knowledge of inverse jacobian. The model-free sliding PD force controller is used to compensate nonlinear dynamics of each robot and the residual error dynamics is finally canceled by a chattering-free cartesian sliding mode to guarantee convergence of position and force tracking errors. It is important notice that inverse kinematics are avoided by synthesized cartesian, rather than joint error sliding surfaces, thus the commuting manifold does not depend on the jacobian, therefore, the system is robust against jacobian uncertainty. Simulations study of two robots manipulating a constrained object shows that system is robust under parametric uncertainty of robots.