This letter proposes a hybrid learning and optimization framework for mobile manipulators for complex and physically interactive tasks. The framework exploits an admittance-type physical interface to obtain intuitive and simplified human demonstrations and Gaussian Mixture Model (GMM)/Gaussian Mixture Regression (GMR) to encode and generate the learned task requirements in terms of position, velocity, and force profiles. Next, using the desired trajectories and force profiles generated by GMM/GMR, the impedance parameters of a Cartesian impedance controller are optimized online through a Quadratic Program augmented with an energy tank to ensure the passivity of the controlled system. Two experiments are conducted to validate the framework, comparing our method with two approaches with constant stiffness (high and low). The results showed that the proposed method outperforms the other two cases in terms of trajectory tracking and generated interaction forces, even in the presence of disturbances such as unexpected end-effector collisions.

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