A Minimax Scheduling Framework for Inertially-Constrained Multi-Agent Systems

Distributed Scheduling at Non-Signalized Intersections with Mixed Cooperative and Non-Cooperative Vehicles

“…In our previous work [14], we considered the special case with only one cooperative vehicle (i.e., S coop = {s 0 }), and formulated a minimax policy for s 0 to optimize the worstcase performance against the trajectory uncertainty of the non-cooperative vehicles. Although the minimax policy is applicable in the general case with multiple cooperative vehicles, it is inefficient since it fails to make use of the cooperation among the vehicles in S coop .…”

“…The main challenge in this stage is that each vehicle needs to consider the existence of both cooperative and noncooperative vehicles. Specifically, direct following policies for fully cooperative systems such as [18] cannot achieve a robust performance when non-cooperative vehicles exist, while the minimax policy proposed in [14] is designed for fully non-cooperative systems and fails to take advantage of the cooperation of vehicles. To tackle the challenge, we propose a short-horizon trajectory planning policy by modifying the minimax policy, which can exploit the benefit of cooperation while maintaining the robustness against noncooperative vehicles.…”

“…The proposed short-horizon trajectory planning policy for s i at time t i,k is shown in Algorithm 2. First, similar to the minimax policy in [14], Algorithm 2 is based on the following minimax optimization problem (see Line 11) arg min…”

“…Specifically, the objective function V (p, v; K) provides an evaluation of the state p, v under the situation information K; the inner optimization aims to find the worst case K k+1 based on the current knowledge J i,k ; and the outer minimization aims to find the target state p tar , v tar resulting in the best worstcase performance. Detailed definitions of these variables can be found in [14]. Despite the similarities above, the following two differences can also be noted, which reflect how the proposed policy deals with the cooperative vehicles.…”

“…• Different from [14], the minimax optimization (10) is not always adopted in Algorithm 2. Specifically, Lines 1-2 show that s i will directly adopt the maximum acceleration without solving the optimization problem after its state enters the region…”