Sequential Composition for Navigating a Nonholonomic Cart in the Presence of Obstacles

In this study, we consider the problem of safely steering a planar nonholonomic cart around obstacles to reach a goal state. We achieve this by the decomposition of the free workspace into triangular tori and generation of local smooth feedback laws that drive the robot from one cell to an adjoining cell. These control laws exploit the fact that for nonholonomic systems, one can generate smooth controllers to reach a particular subset in the configuration space, even though smooth feedback laws cannot be obtained to reach a particular state. These local controllers are then sequenced using discrete motion planning algorithms like A* or incremental D* to reach the goal. We demonstrate the practical efficacy of this methodology by applying it to two experimental platforms: (1) a differential drive robot in which inertial effects are negligible and (2) a hexapedal robot in which inertial effects are significant but difficult to model. In both cases, we use the abstraction of a planar kinematic cart with process noise to develop feedback controllers. We present successful implementation of the controllers to navigate the hexapedal robot in both static and dynamic environments with obstacles.