Omnidirectional Platforms for Gait Training: Admittance-Shaping Control for Enhanced Mobility

We present a design method for the admittance control of a class of omnidirectional mobile platforms. Holonomic behavior of the platform is accomplished by a steering system that is itself subject to nonholonomic constraints. The proposed application of this type of platform, henceforth the "walker", is as an assistive device for human gait rehabilitation. Therefore, the control design objectives are to guarantee the stability of the coupled system formed by the robotic platform and the human body, and to maximize mobility for the user by reducing the robot's apparent inertia. First, we show how feedback linearization of a reduced-order model of the system, combined with a smooth trajectory-tracking control, achieves global asymptotic stability of the tracking error. Then we show how compliance in the robot limits the amount of inertia reduction that can be achieved before instability occurs. We address this problem with a control design method that maximizes the amplitude of the system's admittance over a useful range of frequencies. Using root locus analysis and sensitivity transfer functions, we find an optimal value for the virtual mass in the admittance model, representing the best tradeoff between two oscillatory modes. The walker's admittance vs. frequency function is then corrected via a complementary sensor input, namely, the user's torque on the sagittal plane. A second layer of control provides the walker's therapeutic action, consisting of a variable horizontal force that aids propulsion of the user's body. The level of assistive force is modulated with the patient's gait speed and turning rate to ensure easy adaptation. The control design was validated through an experiment involving human users walking in a prototype of the mobile platform.