ESC-MRAC of MIMO systems for constrained robotic motion tasks in deformable environments

Performance of constrained movements in multiple directions of a workspace simultaneously and in presence of uncertainty is a great challenge for robots. Achieving such tasks by employing control policies which are fully determined a priori and do not take into account the system uncertainty can cause undesired stress on the robot end-effector or the environment and result in poor performance. Instead, a sophisticated control policy is required, which can adjust to the varying conditions of a task while taking into account the coupling of motion dynamics between different directions of movement. To this aim, in this paper, we propose a MIMO Extremum Seeking Control (ESC)-Model Reference Adaptive Control (MRAC) approach with the view of executing fine motion tasks in presence of uncertain task dynamics. ESC enhances robustness of the system to non-parametric uncertainties compared to single MRAC. The proposed approach ensures state tracking as well as optimization of a global state-dependent cost criterion in all directions of movement. We evaluate our approach in simulations and in a real-world robotic engraving task.