A New Projected Active Set Conjugate Gradient Approach for Taylor-Type Model Predictive Control: Application to Lower Limb Rehabilitation Robots With Passive and Active Rehabilitation - Shi, Tian; Tian, Yantao; Sun, Zhongbo; Zhang, Bangcheng; Pang, Zaixiang; Yu, Junzhi; Zhang, Xin (Frontiers in Neurorobotics, 2020)
In this paper, an echo state network (ESN) is firstly established to realize intention recognition for human-machine interactive control of lower-limb rehabilitation robots. A three-order Taylor-type numerical differentiation formula is utilized to linearize and discretize constrained conditions of model predictive control (MPC), which can be generalized from lower limb rehabilitation robots. Meanwhile, a new numerical approach projecting active set conjugate gradient approach is proposed, analyzed and investigated to solve MPC. This numerical approach not only incorporates both active set and conjugate gradient approach, but also utilizes projective operator which can guarantee that the equality constraints are always satisfied. Furthermore, a rigorous proof of feasibility and global convergence also indicate that the proposed approach can effectively solve MPC with equality and bound constraints. Finally, simulation results are reported and analyzed to substantiate that ESN can accurately identify motion intention, and the projected active set conjugate gradient approach is feasible and effective for lower-limb rehabilitation robot of MPC with passive and active rehabilitation training.