Competition-Aware Decision-Making Approach for Mobile Robots in Racing Scenarios

TL;DR

The paper addresses competitive decision‑making for autonomous racing where the ego robot must block an overtaking opponent. It introduces a level‑K game‑theoretic framework with online opponent level estimation and an adaptive trajectory mixing strategy that blends the Level‑K best trajectory with a fail‑safe trajectory to hedge against level changes. The method relies on a library of nine candidate trajectories generated by fifth‑order polynomial plans and a zero‑sum reward structure combining $R_{pos}$, $R_{rel}$, and $R_{block}$, solved via a level‑K payoff matrix and online BELIEF updates $P^o(k)$. The ego uses an MPC tracker to execute the chosen trajectory, and performance is validated in simulations and human‑in‑the‑loop experiments, showing superior blocking rates compared to a conventional Level‑K approach. The results suggest applicability to real‑time competitive robotics and human–robot competition contexts.

Abstract

This paper presents a game-theoretic strategy for racing, where the autonomous ego agent seeks to block a racing opponent that aims to overtake the ego agent. After a library of trajectory candidates and an associated reward matrix are constructed, the optimal trajectory in terms of maximizing the cumulative reward over the planning horizon is determined based on the level-K reasoning framework. In particular, the level of the opponent is estimated online according to its behavior over a past window and is then used to determine the trajectory for the ego agent. Taking into account that the opponent may change its level and strategy during the decision process of the ego agent, we introduce a trajectory mixing strategy that blends the level-K optimal trajectory with a fail-safe trajectory. The overall algorithm was tested and evaluated in various simulated racing scenarios, which also includes human-in-the-loop experiments. Comparative analysis against the conventional level-K framework demonstrates the superiority of our proposed approach in terms of overtake-blocking success rates.

Figures (6)

• Figure 1: Example of two-players racing scenario with illustrations of possible trajectories based on the strategies.
• Figure 2: The example of the opponent's sudden level change. (a) The ego robot is overtaken by the opponent due to the reaction delay. (b) The ego robot blocks the overtaking attempt by following a mixed trajectory.
• Figure 3: Experimental setup. (a) The experiment involving human participants to control the opponent robot, (b) The process of the experiment.
• Figure 4: The representative interacting case of the two robots racing scenario, where the blue square is the ego robot controlled by our approach, and the red square is the opponent robot controlled by three different approaches. The lines in front of the robots are planned trajectories (red: best, black: fail-safe, blue: mixed). (a) The ego robot blocks in the way of the opponent. (b) The ego robot follows the mixed trajectory to block the opponent's predicted trajectory. (c) The ego robot follows the trajectory to block the opponent who is already far from the ego robot, the mixed trajectory overlaps with the best trajectory.
• Figure 5: The estimated belief of the opponent's level for representative scenarios.