Predictive adaptive control of multiple robots in cooperative motion

In this paper we address the problem of controlling multiple non redundant robots manipulating a rigid object cooperatively when the parameters of the robots and the parameters of the load are uncertain. We propose a controller that takes into account the dynamics of both the load and the manipulators. The linearity of the dynamics of the robots and the load, with respect to the unknown parameters, is exploited during the derivation of the parameter's adaptation scheme. In order to design control and update laws that do not require the measurements of the joint accelerations or the load acceleration, the dynamics of both the robots and the load are filtered through a stable first order filter. Two prediction error vectors are then defined as the difference between the measured filtered dynamics and the predicted filtered dynamics of both the robots and the load. The least-squares estimation method or gradient method can be used to estimate the parameters of the multi-robot system from the prediction errors. We then develop a controller that is based on the cancellation of the nonlinearities. The proposed controller guarantees asymptotic tracking of the load trajectories and also guarantees asymptotic tracking of the internal forces trajectories.