RESUMEN
Multi-agent systems are utilized more often in the research community and industry, as they can complete tasks faster and more efficiently than single-agent systems. Therefore, in this paper, we are going to present an optimal approach to the multi-agent navigation problem in simply connected workspaces. The task involves each agent reaching its destination starting from an initial position and following an optimal collision-free trajectory. To achieve this, we design a decentralized control protocol, defined by a navigation function, where each agent is equipped with a navigation controller that resolves imminent safety conflicts with the others, as well as the workspace boundary, without requesting knowledge about the goal position of the other agents. Our approach is rendered sub-optimal, since each agent owns a predetermined optimal policy calculated by a novel off-policy iterative method. We use this method because the computational complexity of learning-based methods needed to calculate the global optimal solution becomes unrealistic as the number of agents increases. To achieve our goal, we examine how much the yielded sub-optimal trajectory deviates from the optimal one and how much time the multi-agent system needs to accomplish its task as we increase the number of agents. Finally, we compare our method results with a discrete centralized policy method, also known as a Multi-Agent Poli-RRT* algorithm, to demonstrate the validity of our method when it is attached to other research algorithms.
RESUMEN
In this paper, we address the trajectory-/target-tracking and obstacle-avoidance problem for nonholonomic mobile robots subjected to diamond-shaped velocity constraints and predefined output performance specifications. The proposed scheme leverages the adaptive performance control to dynamically adjust the user-defined output performance specifications, ensuring compliance with input and safety constraints. A key feature of this approach is the integration of multiple constraints into a single adaptive performance function, governed by a simple adaptive law. Additionally, we introduce a robust velocity estimator with a priori-determined performance attributes to reconstruct the unmeasured trajectory/target velocity. Finally, we validate the effectiveness and robustness of the proposed control scheme, through extensive simulations and a real-world experiment.
RESUMEN
In control theory, reactive methods have been widely celebrated owing to their success in providing robust, provably convergent solutions to control problems. Even though such methods have long been formulated for motion planning, optimality has largely been left untreated through reactive means, with the community focusing on discrete/graph-based solutions. Although the latter exhibit certain advantages (completeness, complicated state-spaces), the recent rise in Reinforcement Learning (RL), provides novel ways to address the limitations of reactive methods. The goal of this paper is to treat the reactive optimal motion planning problem through an RL framework. A policy iteration RL scheme is formulated in a consistent manner with the control-theoretic results, thus utilizing the advantages of each approach in a complementary way; RL is employed to construct the optimal input without necessitating the solution of a hard, non-linear partial differential equation. Conversely, safety, convergence and policy improvement are guaranteed through control theoretic arguments. The proposed method is validated in simulated synthetic workspaces, and compared against reactive methods as well as a PRM and an RRTâ approach. The proposed method outperforms or closely matches the latter methods, indicating the near global optimality of the former, while providing a solution for planning from anywhere within the workspace to the goal position.