Mobile robotic systems, in which manipulators are mounted on a moving base, are to be employed in performing different tasks, e. g. astronaut assistance in space, rescuing operations, nursing, book keeping, storing, etc. To manipulate an object with of several cooperating manipulators, the Multiple
Impedance control (MIC) as a Model-Based algorithm enforces a designated impedance on all cooperating manipulators, the manipulated object, and the moving base if applied on a mobile robotic system. To apply model-based control laws, it is needed to extract explicit system dynamic model. In this paper, using Lagrange coefficients, the non-slipping non-holonomic constraint is applied on the dynamic equations for robotic systems with free moving base. Then, the Lagrange coefficients are omitted from the motion equation by using “Natural Orthogonal Complement” method and the explicit motion equations are obtained for mobile robotic system with constrained base. By designing the appropriate path of motion, the multiple impedance control law is applied on a robotic systems with two manipulators while the moving base is driven with two differentially driver wheels. The simulation results reveal good tracking performance even in the presence of disturbances and impact due to contact with the environment.
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