Real-time optimization of an ellipsoidal trajectory orientation using muscle effort with Extremum Seeking Control

We present an approach for real-time model-free optimization of the orientation of the elliptical trajectory. The performance is evaluated in simulation and experimental stages. Our model-free approach is based on the use of Extremum Seeking Control (ESC) as the real-time optimizer. The experimental stage is performed using a 4 degrees-of-freedom robot and its impedance control system to create advanced exercise protocols whereby the user is asked to follow a path against the machine's neutral path and resistance. Another model-free approach based on the use of the global optimizer Biogeography-based optimization (BBO) was previously reported for simulation results. This last framework has a good performance as a result of exhaustive searches but with a high computational cost limiting its use on real-time experiments. The performance of the ESC approach was validated by comparing the results with those of BBO using five different arm models representing real human arms. In the real-time experiments, muscle activations representing the participation of each muscle in the training activity were measured with electromyography sensors (EMG) and real-time processed from raw signals. The muscle objective can be professionally selected by a therapist to emphasize or de-emphasize certain muscle groups. The robot establishes a zero-effort circular path, and the subject is asked to follow an elliptical trajectory. The control system produces a user-defined stiffness between the deviations from the neutral path and the force/torque applied by the subject. The results show that the framework was able to successfully find the optimal ellipsoidal orientation converging to similar solutions in short period trials of 50 s.