Encircling General 2-D Boundaries by Mobile Robots with Collision Avoidance: A Vector Field Guided Approach

The ability to automatically encircle boundaries with mobile robots is crucial for tasks such as border tracking and object enclosing. Previous research has primarily focused on regular boundaries, often assuming that their geometric equations are known in advance, which is not often the case in practice. In this paper, we investigate a more general case and propose an algorithm that addresses geometric irregularities of boundaries without requiring prior knowledge of their analytical expressions. To achieve this, we develop a Fourier-based curve fitting method for boundary approximation using sampled points, enabling parametric characterization of general 2-D boundaries. This approach allows star-shaped boundaries to be fitted into polar-angle-based parametric curves, while boundaries of other shapes are handled through decomposition. Then, we design a vector field (VF) to achieve the encirclement of the parameterized boundary, wherein a polar radius error is introduced to measure the robot's ``distance'' to the boundary. The controller is finally synthesized using a control barrier function and quadratic programming to mediate some potentially conflicting specifications: boundary encirclement, obstacle avoidance, and limited actuation. In this manner, the VF-guided reference control not only guides the boundary encircling action, but can also be minimally modified to satisfy obstacle avoidance and input saturation constraints. Simulations and experiments are presented to verify the performance of our new method, which can be applied to mobile robots to perform practical tasks such as cleaning chemical spills and environment monitoring.

Collision-Free Navigation of Wheeled Mobile Robots: An Integrated Path Planning and Tube-Following Control Approach

In this paper, an integrated path planning and tube-following control scheme is proposed for collision-free navigation of a wheeled mobile robot (WMR) in a compact convex workspace cluttered with sufficiently separated spherical obstacles. An analytical path planning algorithm is developed based on Bouligand's tangent cones and Nagumo's invariance theorem, which enables the WMR to navigate towards a designated goal location from almost all initial positions in the free space, without entering into augmented obstacle regions with safety margins. We further construct a virtual "safe tube" around the reference trajectory, ensuring that its radius does not exceed the size of the safety margin. Subsequently, a saturated adaptive controller is designed to achieve safe trajectory tracking in the presence of disturbances. It is shown that this tube-following controller guarantees that the WMR tracks the reference trajectory within the predefined tube, while achieving uniform ultimate boundedness of both the position tracking and parameter estimation errors. This indicates that the WMR will not collide with any obstacles along the way. Finally, we report simulation and experimental results to validate the effectiveness of the proposed method.