Dynamic game arises as a powerful paradigm for multi-robot planning, for which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, as real-world robots need to operate and satisfy constraints under uncertainty. Existing methods for solving stochastic games handle chance constraints using exponential penalties with hand-tuned weights. However, finding a suitable penalty weight is nontrivial and requires trial and error. In this paper, we propose the chance-constrained iterative linear-quadratic stochastic games (CCILQGames) algorithm. CCILQGames solves chance-constrained stochastic games using the augmented Lagrangian method. We evaluate our algorithm in three autonomous driving scenarios, including merge, intersection, and roundabout. Experimental results and Monte Carlo tests show that CCILQGames can generate safe and interactive strategies in stochastic environments.

翻译：动态博弈作为多机器人规划的强大范式应运而生，其中安全约束的满足至关重要。约束随机博弈尤其受到关注，因为现实世界的机器人需要在不确定性下运行并满足约束。现有求解随机博弈的方法使用指数惩罚与手动调整的权重来处理机会约束。然而，找到合适的惩罚权重并非易事，需要反复试验。本文提出了机会约束迭代线性二次型随机博弈（CCILQGames）算法。CCILQGames使用增广拉格朗日方法求解机会约束随机博弈。我们在三种自动驾驶场景（包括合流、交叉路口和环岛）中评估了该算法。实验和蒙特卡洛测试结果表明，CCILQGames能够在随机环境中生成安全且具有交互性的策略。