  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.
