Guaranteed Obstacle Avoidance for Multi-Robot Operations With Limited Actuation: A Control Barrier Function Approach

Online Decentralized Decision Making With Inequality Constraints: An ADMM approach

“…This is sufficient to guarantee safety, since under (19), any nonnegative h will remain nonnegative. In particular, [10] presents a CBF based on backup policies, which is applicable to multiagent problems and the feasibility of the decentralized CBF QP is guaranteed when h ≥ 0. To be specific, consider N agents with dynamics x i = f i (x i ) + g i (x i )u i , where x i and u i are the state and input of agent i.…”

“…Fig. 3: Total constraint violation of the constraint splitting method used in [10], the Prox-JADMM, and the optimal solution solved with centralized optimization Fig. 4: Effect of warm start on convergence where u i contains u i and u i j , the local copies of the input of all its neighbors.…”

“…Fig. 3 shows the performance comparison of the Prox-JADMM algorithm with the benchmark in [10] and the optimal solution. The total constraint violation of Prox-JADMM is always smaller than the benchmark, and very close to the optimal solution, as Theorem 1 predicts.…”

“…The goal is to search for the solution that minimizes the violation. Examples of such problems include motion planning for multiple agents [9], [10], [11], decentralized model predictive control [12], and decentralized coordination for power grids [13], [14]. Moreover, we consider the case where the decentralized decision making problem is solved repeatedly with gradually changing data, i.e., the inequality constraints and local objective functions changes gradually between successive time steps.…”

“…Warm start online Prox-JADMM1: t ← 0, k ← 0 2: {x 0 i } ← 0, y 0 ← 0 3: while NOT TERMINATE do 4: Obtain {F i }[t], calculate L 5: for k = 0 : M do 6:Prox-JADMM update following(10) …”