Collaborative Satisfaction of Long-Term Spatial Constraints in Multi-Agent Systems: A Distributed Optimization Approach (extended version)
Farhad Mehdifar, Mani H. Dhullipalla, Charalampos P. Bechlioulis, Dimos V. Dimarogonas
TL;DR
This work tackles collaborative satisfaction of long-term spatial constraints in multi-agent systems by first formulating a centralized objective that increases with constraint satisfaction and yields a least-violating formation when infeasible. It then develops a distributed optimization framework using log-sum-exp smoothing to approximate the centralized problem, yielding a sum of local objective functions \(f(\bm{x}) = \sum_i f_i(\bm{x}_i,\bm{x}_{\mathcal{I}_i})\) and a consensus-based controller that drives agents toward the distributed optimum \(\hat{\bm{x}}^{\ast}\). The approach provides conditions for (strict) convexity of the global objective, a practical continuous-time protocol, and a mechanism to avoid numerical overflow via a time-varying smoothing parameter. Simulations with three agents demonstrate feasibility, convergence to optimal formations when feasible, and meaningful least-violating or rendezvous behavior under infeasibility or nonconvexity. Overall, the method enables scalable, privacy-preserving cooperative coordination under spatiotemporal constraints in MAS.
Abstract
This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents with whom they may or may not have direct communication. These constraints need to be satisfied asymptotically or after an unknown finite time. The agents' objective is to collectively achieve a formation that fulfills all constraints. The problem is initially framed as a centralized unconstrained optimization, where the solution yields the optimal configuration by maximizing an objective function that reflects the degree of constraint satisfaction. This function encourages collaboration, ensuring agents help each other meet their constraints while fulfilling their own. When the constraints are infeasible, agents converge to a least-violating solution. A distributed consensus-based optimization scheme is then introduced, which approximates the centralized solution, leading to the development of distributed controllers for single-integrator agents. Finally, simulations validate the effectiveness of the proposed approach.