Model Predictive Control with Visibility Graphs for Humanoid Path Planning and Tracking Against Adversarial Opponents

In this paper we detail the methods used for obstacle avoidance, path planning, and trajectory tracking that helped us win the adult-sized, autonomous humanoid soccer league in RoboCup 2024. Our team was undefeated for all seated matches and scored 45 goals over 6 games, winning the championship game 6 to 1. During the competition, a major challenge for collision avoidance was the measurement noise coming from bipedal locomotion and a limited field of view (FOV). Furthermore, obstacles would sporadically jump in and out of our planned trajectory. At times our estimator would place our robot inside a hard constraint. Any planner in this competition must also be be computationally efficient enough to re-plan and react in real time. This motivated our approach to trajectory generation and tracking. In many scenarios long-term and short-term planning is needed. To efficiently find a long-term general path that avoids all obstacles we developed DAVG (Dynamic Augmented Visibility Graphs). DAVG focuses on essential path planning by setting certain regions to be active based on obstacles and the desired goal pose. By augmenting the states in the graph, turning angles are considered, which is crucial for a large soccer playing robot as turning may be more costly. A trajectory is formed by linearly interpolating between discrete points generated by DAVG. A modified version of model predictive control (MPC) is used to then track this trajectory called cf-MPC (Collision-Free MPC). This ensures short-term planning. Without having to switch formulations cf-MPC takes into account the robot dynamics and collision free constraints. Without a hard switch the control input can smoothly transition in cases where the noise places our robot inside a constraint boundary. The nonlinear formulation runs at approximately 120 Hz, while the quadratic version achieves around 400 Hz.