Flip Co-op: Cooperative Takeovers in Shared Autonomy

Shared autonomy requires principled mechanisms for allocating and transferring control between a human and an autonomous agent. Existing approaches often rely on blending control inputs between human and autonomous agent or switching rules, which lack theoretical guarantees. This paper develops a game-theoretic framework for modeling cooperative takeover in shared autonomy. We formulate the switching interaction as a dynamic game in which authority is embedded directly into the system dynamics, resulting in Nash equilibrium(NE)-based strategies rather than ad hoc switching rules. We establish the existence and characterization of NE in the space of pure takeover strategies under stochastic human intent. For the class of linear-quadratic systems, we derive closed-form recursions for takeover strategies and saddle-point value functions, providing analytical insight and efficient computation of cooperative takeover policies. We further introduce a bimatrix potential game reformulation to address scenarios where human and autonomy utilities are not perfectly aligned, yielding a unifying potential function that preserves tractability while capturing intent deviations. The framework is applied to a vehicle trajectory tracking problem, demonstrating how equilibrium takeover strategies adapt across straight and curved path segments. The results highlight the trade-off between human adaptability and autonomous efficiency and illustrate the practical benefits of grounding shared autonomy in cooperative game theory.