An Adaptive Assistance Controller to Optimize the Exoskeleton Contribution in Rehabilitation

In this paper, we present a novel adaptation rule to optimize the exoskeleton assistance in rehabilitation tasks. The proposed method adapts the exoskeleton contribution to user impairment severity without any prior knowledge about the user motor capacity. The proposed controller is a combination of an adaptive feedforward controller and a low gain adaptive PD controller. The PD controller guarantees the stability of the human-exoskeleton system during feedforward torque adaptation by utilizing only the human-exoskeleton joint positions as the sensory feedback for assistive torque optimization. In addition to providing a convergence proof, in order to study the performance of our method we applied it to a simplified 2-DOF model of human-arm and a generic 9-DOF model of lower limb to perform walking. In each simulated task, we implemented the impaired human torque to be insufficient for the task completion. Moreover, the scenarios that violate our convergence proof assumptions are considered. The simulation results show a converging behavior for the proposed controller; the maximum convergence time of 20 s is observed. In addition, a stable control performance that optimally supplements the remaining user motor contribution is observed; the joint angle tracking error in steady condition and its improvement compared to the start of adaptation are as follows: shoulder 0.96±2.53° (76%); elbow −0.35±0.81° (33%); hip 0.10±0.86° (38%); knee −0.19±0.67° (25%); and ankle −0.05±0.20° (60%). The presented simulation results verify the robustness of proposed adaptive method in cases that differ from our mathematical assumptions and indicate its potentials to be used in practice.

Sparse Solutions by a Quadratically Constrained ℓq (0 < q < 1) Minimization Model

Finding sparse solutions to a system of equations and/or inequalities is an important topic in many application areas such as signal processing, statistical regression and nonparametric modeling. Various continuous relaxation models have been proposed and widely studied to deal with the discrete nature of the underlying problem. In this paper, we propose a quadratically constrained [Formula: see text] (0 < q < 1) minimization model for finding sparse solutions to a quadratic system. We prove that solving the proposed model is strongly NP-hard. To tackle the computation difficulty, a first order necessary condition for local minimizers is derived. Various properties of the proposed model are studied for designing an active-set-based descent algorithm to find candidate solutions satisfying the proposed condition. In addition to providing a theoretical convergence proof, we conduct extensive computational experiments using synthetic and real-life data to validate the effectiveness of the proposed algorithm and to show the superior capability in finding sparse solutions of the proposed model compared with other known models in the literature. We also extend our results to a quadratically constrained [Formula: see text] (0 < q < 1) minimization model with multiple convex quadratic constraints for further potential applications. Summary of Contribution: In this paper, we propose and study a quadratically constrained [Formula: see text] minimization (0 < q < 1) model for finding sparse solutions to a quadratic system which has wide applications in sparse signal recovery, image processing and machine learning. The proposed quadratically constrained [Formula: see text] minimization model extends the linearly constrained [Formula: see text] and unconstrained [Formula: see text]-[Formula: see text] models. We study various properties of the proposed model in aim of designing an efficient algorithm. Especially, we propose an unrelaxed KKT condition for local/global minimizers. Followed by the properties studied, an active-set based descent algorithm is then proposed with its convergence proof being given. Extensive numerical experiments with synthetic and real-life Sparco datasets are conducted to show that the proposed algorithm works very effectively and efficiently. Its sparse recovery capability is superior to that of other known models in the literature.