Guided trajectory planning involves a leader robot strategically directing a follower robot to collaboratively reach a designated destination. However, this task becomes notably challenging when the leader lacks complete knowledge of the follower's decision-making model. There is a need for learning-based methods to effectively design the cooperative plan. To this end, we develop a Stackelberg game-theoretic approach based on the Koopman operator to address the challenge. We first formulate the guided trajectory planning problem through the lens of a dynamic Stackelberg game. We then leverage Koopman operator theory to acquire a learning-based linear system model that approximates the follower's feedback dynamics. Based on this learned model, the leader devises a collision-free trajectory to guide the follower using receding horizon planning. We use simulations to elaborate on the effectiveness of our approach in generating learning models that accurately predict the follower's multi-step behavior when compared to alternative learning techniques. Moreover, our approach successfully accomplishes the guidance task and notably reduces the leader's planning time to nearly half when contrasted with the model-based baseline method.

翻译：导引轨迹规划涉及领航机器人战略性地引导跟随机器人协同到达指定目标点。然而，当领航者缺乏对跟随者决策模型的完整认知时，该任务将变得尤为具有挑战性。为此需要基于学习方法有效设计协同方案。针对这一挑战，我们提出了一种基于Koopman算子的Stackelberg博弈方法。首先通过动态Stackelberg博弈视角构建导引轨迹规划问题，进而利用Koopman算子理论获取学习型线性系统模型以近似跟随者的反馈动态。基于该学习模型，领航者采用滚动时域规划生成无碰撞轨迹引导跟随者。通过仿真实验，我们验证了该方法相较于其他学习技术在生成精确预测跟随者多步行为的学习模型方面的有效性。此外，与基于模型的基线方法相比，本方法成功完成了导引任务，并将领航者的规划时间显著缩短近半。