Stochastic Modeling And Control Of The Omnidirectional Rehabilitative Training Walker

As the aging of population, an accumulating number of people were suffering from walking impairments, which were caused by the diseases of the brain nervous system and motor nervous system. Due to the limited medical resources, the walking rehabilitative robot has been developed. Rehabilitative robots are highly nonlinear and strong coupling, and easily affected by the factors of shift in gravity center, actuator fault, accuracy of speed sensor measurement, and position sensor complete measurement when it tracks the training path prescribed physical therapists, which hardly achieved an accurate trajectory tracking. In order to improve the tracking accuracy of rehabilitative robots, in the prevent paper, with an omnidirectional rehabilitative training walker as the research object, the problem of trajectory tracking is studied based on stochastic control theory, and the main contents are as follows:By turning the random parameters that were caused by the shift in the center of gravity into the random disturbance, and combined with the stochastic theory, a stochastic model of the omnidirectional rehabilitative walker was proposed. An state feedback controller was designed based on the stochastic model above, such that the trajectory tracking error system was exponentially practically mean square stable, and the parameters were designed such that the tracking error and its derivative tend toward an arbitrarily small neighborhood of zero. The simulation results demonstrate that the omnidirectional rehabilitative training walker would track the predetermined trajectory accurately by the designed state feedback controller.The faulty actuator was separated from the control matrix of the stochastic model above that would be considered in relation to the extrinsic bounded interference, and an adaptive tracking controller was designed based on the criteria of the stochastic stability. Stability analysis proved that the controller is applied, such that the tracking error system was exponentially practically mean square stable. parameters of the controller and control law can be designed such that the tracking error and its derivative tend toward an arbitrarily small neighborhood of zero. The simulation results demonstrate that the designed adaptive fault tolerant controller based on stochastic model can handle simultaneously the shift in center of gravity and actuator faults.A mathematical model is proposed to describe the phenomena of incomplete output measurements,which was used for an design of output observer. An output feedback controller was designed based on the information of an speed observer. Stability analysis proved that the closed loop system consisted of output observer errors, speed observer errors, and trajectory tracking errors was exponentially practically mean square stable, and the parameters were adjusted such that the tracking error and its derivative tend toward an arbitrarily small neighborhood of zero. The simulation results show that the output observer, speed observer and output feedback controller were effective.