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.

Leader-Follower Formation Control of Perturbed Nonholonomic Agents along Parametric Curves with Directed Communication

In this paper, we propose a novel formation controller for nonholonomic agents to form general parametric curves. First, we derive a unified parametric representation for both open and closed curves. Then, a leader-follower formation controller is designed to form the parametric curves. We consider directed communications and constant input disturbances rejection in the controller design. Rigorous Lyapunov-based stability analysis proves the asymptotic stability of the proposed controller. Detailed numerical simulations and experimental studies are conducted to verify the performance of the proposed method.

Robust Integral Consensus Control of Multi-Agent Networks Perturbed by Matched and Unmatched Disturbances: The Case of Directed Graphs

This work presents a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree. We propose new robust controllers to solve the consensus and synchronization problems when the systems are under the effects of matched and unmatched disturbances. In both problems, we present simple continuous controllers, whose integral actions allow us to handle the disturbances. A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented. To assess the performance of our result, a representative simulation study is presented.

Simultaneous Position-and-Stiffness Control of Underactuated Antagonistic Tendon-Driven Continuum Robots

Continuum robots have gained widespread popularity due to their inherent compliance and flexibility, particularly their adjustable levels of stiffness for various application scenarios. Despite efforts to dynamic modeling and control synthesis over the past decade, few studies have focused on incorporating stiffness regulation in their feedback control design; however, this is one of the initial motivations to develop continuum robots. This paper aims to address the crucial challenge of controlling both the position and stiffness of a class of highly underactuated continuum robots that are actuated by antagonistic tendons. To this end, the first step involves presenting a high-dimensional rigid-link dynamical model that can analyze the open-loop stiffening of tendon-driven continuum robots. Based on this model, we propose a novel passivity-based position-and-stiffness controller adheres to the non-negative tension constraint. To demonstrate the effectiveness of our approach, we tested the theoretical results on our continuum robot, and the experimental results show the efficacy and precise performance of the proposed methodology.