Curvature-Constrained Vector Field for Motion Planning of Nonholonomic Robots
Yike Qiao, Xiaodong He, An Zhuo, Zhiyong Sun, Weimin Bao, Zhongkui Li
AI summary
Problem
Existing vector field planners fail to incorporate curvature constraints due to the tight coupling between field design and tracking control under limited actuation, often causing trajectory violations or singularities. Open-loop methods also lack robustness to real-world deviations.
Approach
The method partitions the workspace to blend sink, vortex, and source flows into a curvature-bounded vector field, paired with a saturated control law that uses dynamic gains to maintain tracking accuracy even when actuation limits are hit.
Key results
- CVF constructed with a stable limit cycle ensuring bounded, continuous curvature
- Saturated control law with dynamic gains stabilizes orientation error under actuation limits
- Explicit co-design conditions proven to guarantee almost global convergence to target limit sets
- 100% convergence success in simulations and successful real-world deployment on UGVs and UAVs
Why it matters
Provides a robust, real-time planning framework for curvature-constrained robots like UGVs and UAVs, eliminating the need for frequent replanning and ensuring safe navigation in dynamic environments.
Abstract
Vector fields are advantageous in handling nonholo- nomic motion planning, as they provide the robot with reference orientation across the workspace. However, additionally incorpo- rating curvature constraints presents challenges due to the inter- connection 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 formu- late 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 kinemat- ically 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 sce- narios.