Passive robotic walker path following with bang-bang hybrid control paradigm

This paper presents a control algorithm that steers a robotic walking assistant along a planned path using electromechanical brakes. The device is modeled as a Dubins' car, i.e., a wheeled vehicle that moves only forward in the plane and has a limited turning radius. In order to reduce the cost of the hardware, no force sensor is employed. This feature hampers the application of control algorithms based on a modulated braking action. A viable solution is based on the application of on/off braking action, thus forcing the vehicle to turn with a fixed turning radius. In order to avoid the annoying chattering behaviour, which is the inevitable companion of all bang-bang solutions, we propose a hybrid controller based on three discrete states that rule the application of the braking action. The resulting feedback controller secures a gentle convergence of the user toward the planned path and his/her steady progress towards the destination. This is obtained by using two independent hystereses thresholds, the first one associated with the approaching phase and the second with the following phases. The system convergence toward the path is formally proved. Simulations and experiments show the effectiveness of the proposed approach and the good level of comfort for the user.