Model predictive control with angular acceleration constraint of proportional servo-hydraulic lower extremity robotic device

Abstract

Lower Extremity Robotic Device (LERD) is a four-degree of freedom hydraulic exoskeleton that assists the paralysed patient to walk. The nonlinear dynamic model of the hydraulic exoskeleton system used in Model Predictive Control (MPC) is challenging to be modelled, especially in the state-space model form. Traditional torque constraint technique restricts the exoskeleton to provide wide variability of wearers’ weight. For a heavy wearer, the torque constraint could limit the system’s performance where the hydraulic force will be cut off when exceeds the predetermined torque. Angular acceleration constraint could be an alternative method to overcome the weight variations among different wearers. However, this technique has not been reported elsewhere in the literature. This study aimed to develop mathematical models of the empiric relationship between the median of absolute angular accelerations and pulse width modulation duty cycle of the LERD exoskeleton to facilitate system interfacing. An optimal motion constrained MPC controller for trajectory tracking was designed first, and the results were benchmarked with Proportional-Integral-Derivative (PID) controller. Using cross-correlation analysis, the dynamic models were then selected and used to analyse the designed controllers. The average absolute trajectory tracking error (AATTE) was chosen as the performance parameter with the AATTE closer to zero-degree reference point indicates better trajectory tracking. Results of the simulation study for both MPC and PID controllers at three different speeds showed that AATTE became farther as the walking speed increased. Benchmarked for simulation result showed that the PID controller produced closer AATTE of all joints compared to the MPC controller at the slowest speed (0.3m/s). However, as the speed increased, the MPC controller achieved closer AATTE of all joints than the PID controller. The simulation results were further validated with an experimental study at 0.3m/s. After cross-correlation analysis between reference and output trajectories, the PID controller has produced all joints’ AATTE of 2.64 degrees nearer to zero degrees than the MPC controller’s AATTE of all joints (2.99 degrees). In overall, the MPC controller exhibits a smoother control signal compared to the PID controller where the latter produces fluid hammer during operation which can harm the wearer and potential to cause possible damage to the exoskeleton system’s components. The proposed control system is able to avoid the need to derive several important parameters such as valve’s orifice area, flow coefficient, frictions, etc. Based on the findings of this study, it can be concluded that the proposed simulation and prototype models together MPC controller are acceptable for use in the exoskeleton control system.