Formation control of multiple agents has attracted many robotic and control researchers recently because of its potential applications in various fields. This paper presents a novel approach to the formation control and obstacle avoidance of multiple rectangular agents with limited communication ranges. The distributed control algorithm is designed by utilizing an artificial potential function. The convergence and stability analysis of the proposed control algorithm is given. The proposed control algorithm can guarantee fast formation performance and no collision among agents. Also, by proposing a potential repulsive function and utilizing it as an obstacle avoidance function, rectangular agents can perfectly avoid obstacles with different shapes and sizes. As a result, the rectangular agents can move together and quickly form a pre-defined shape of formation, such as a straight line, circle, and lattice, etc., while avoiding the obstacles. Simulation results are conducted to demonstrate the effectiveness of the proposed algorithm.

In this technical note, we investigate a solution of the matrix differential Riccati equation that plays an important role in the linear quadratic optimal control problem. Unlike many methods in the literature, the approach that we propose employs the negative definite anti-stabilizing solution of the matrix algebraic Riccati equation and the solution of the matrix differential Lyapunov equation. An illustrative numerical example is provided to show the efficiency of our approach.

Ankle exoskeletons hold potential to augment human walking ability, yet their use in free-living environments has been limited by the absence of practical and effective control strategies that can appropriately adapt to variable terrain. To address this challenge, we derived a novel analytical ankle joint moment estimation model using custom wearable sensors and developed an exoskeleton control scheme to adapt assistance proportional to the biological plantar-flexor moment in real-time for unimpaired individuals and individuals with disabilities who are able to ambulate independently. We validated the controller during level, 5° incline and decline walking, each at multiple speeds; stair ascent; stair descent; and 90° turning (88 ± 3% average accuracy, R = 0.96 ± 0.01 average correlation coefficient). This study demonstrates the ability of the controller to accurately adapt assistance in unimpaired individuals across a wide variety of walking conditions without the need for walking condition classification or real-time assessment of muscle activity. Clinical feasibility testing in four individuals with cerebral palsy suggests that this control method holds promise for incline and stair walking in individuals with mild-to-severe impairment. This ankle-moment-adaptive control system can be used to prescribe ankle exoskeleton assistance that adapts in real-time across the tested conditions.

A variable structure system can be studied using the singular perturbation theory. The discontinuous control that leads to a finite-time reaching of the sliding surface creates fast-time transients analogous to the stable boundary layer dynamics of a singularly perturbed system. As the sliding mode is attained, the slow-time dynamics prevails, just as that of a singularly perturbed system after the boundary layer dynamics fades away. In this technical note, the problem of sliding mode control for singularly perturbed systems in the presence of matched bounded external disturbances is investigated. A composite sliding surface is constructed from solutions of algebraic Lyapunov equations which are derived from both the fast and the slow subsystems. The resultant sliding motion ensures Lyapunov stability with disturbance rejection. Two proposed schemes that ensure the asymptotic stability of the system are presented. The effectiveness of the proposed methods is demonstrated in a numerical example of a magnetic tape control system.

In this article, we address a formation control problem for a group of autonomous robots to track a moving target in the presence of obstacles. In the proposed method, desired formations, which consist of virtual nodes arranged in specific shapes, are first generated. Then, autonomous robots are driven toward these virtual nodes without collisions with each other using a novel control scheme, which is based on artificial force fields. The convergence analysis is shown based on Lyapunov’s stability. The novelty of the proposed approach lies in a new combination of rotational force field and repulsive force field to design a mechanism so that robots can avoid and escape complex obstacle shapes. The effectiveness of the proposed method is illustrated with numerical examples using V-shape and circular shape formations.