Linear time-invariant feedback operator for mobile robot trajectory tracking

In this paper we propose a linear time-invariant (LTI) state feedback operator for nonholonomic mobile robots to track a pre-defined trajectory on a 2D planar region. Designing an on-line smooth state feedback control law is still among the major challenges for solving the trajectory tracking problem of nonholonomic systems including differential drive mobile robots. To address this problem, numerous nonlinear feedback control laws have been proposed to date. Most of these feedback control laws yield online solutions to the trajectory tracking problem with satisfactory tracking errors asymptotically. In most cases, they suffer from an overwhelming degree of computational complexity even to track a 2D trajectory using a simple unicycle-like nonholonomic system. The proposed control law offers an advantage of being smooth and LTI state-feedback in addition to its capability to address problems of partially observed systems. The shortcoming of the proposed control law is that the LTI feedback operator is computed off-line before the robot applies its control signal into the left and right wheels through their actuators. The theoretical results are supported by computer simulations followed by experiments with an e-puck mobile robot.