An energy-optimal framework for assignment and trajectory generation in teams of autonomous agents

Abstract

In this paper, we present a decentralized approach to solving the problem of moving N homogeneous agents into N, or more, goal locations along energy-minimizing trajectories. We propose a decentralized framework which only requires knowledge of the goal locations by each agent. The framework includes guarantees on safety through dynamic constraints, and a method to impose a dynamic, global priority ordering on the agents. A solution to the goal assignment and trajectory generation problems are derived in the form of a binary program and a linear system of equations. We also present the conditions for global optimality and characterize the assumptions under which the algorithm is guaranteed to converge to a unique assignment of agents to goals. Finally, we validate the efficacy of our approach through a numerical simulation in MATLAB.

Beyond Reynolds: A Constraint-Driven Approach to Cluster Flocking

“…Next, we present several properties of the optimal solution to Problem 1. Finding optimality conditions for the solution to Problem 1 can be done by applying the Hamiltonian method [25], which has been achieved for similar types of continuous control problems [1], [9], [26]. However, no known closed-form solution is known to exist for the types of constraints present in Problem 1 [9].…”

“…This is a locally-optimal collision avoidance motion primitive [9]. Otherwise, if boid i violates the task constraint, it instead selects the largest value of t 1 ∈ [t 0 i , t f i ] to activate the task constraint such that: the task constraint is not violated for all t ≤ t 1 and v i (t) = ċi (t) for t ≥ t 1 ; this is a locally optimal solution to the task constraint problem [26].…”

“…By the triangle inequality ||ṡ i (t)|| > 0. The speed profile imposed by all of our motion primitives is a polynomial [26], therefore c i (t) cannot asymptotically approach v i (t). Thus, there exists some finite t 1 ∈ R ≥0 such that ||s i (t 1 )|| = D. Theorem 1.…”