Curvature-Constrained Vector Field for Motion Planning of Nonholonomic Robots

Vector fields are advantageous in handling nonholonomic motion planning, as they provide the robot with reference orientation across the workspace. However, additionally incorporating curvature constraints presents challenges due to the interconnection between the design of the curvature-bounded vector field and the tracking controller under limited actuation. In this article, we present a novel framework to co-develop the vector field and the control law, guiding the nonholonomic robot to the target configuration with curvature-bounded trajectory. First, we formulate the problem by introducing the target positive limit set, which allows the robot to either converge to or pass through the target configuration, depending on its dynamics and the specific tasks. Next, we construct a curvature-constrained vector field (CVF) via blending and embedding elementary flows in the workspace. To track such a CVF, a saturated control law with dynamic gains is proposed, under which the tracking error’s magnitude decreases even when saturation occurs. Under the control law, the kinematically constrained nonholonomic robot is guaranteed to track the reference CVF and converge to the target positive limit set with bounded trajectory curvature. Numerical simulations show that the proposed CVF method outperforms other vector-field-based algorithms. Experiments on Ackermann uncrewed ground vehicles and semiphysical fixed-wing uncrewed aerial vehicles demonstrate that the method can be effectively implemented in real-world scenarios.