Multi-Robot Motion Planning via Dynamic Games

In 2026, my colleague Dr. Timothy Molloy and I began a new project in multi-robot motion planning, focusing on centralized control strategies grounded in dynamic game theory. Students working on the project utilize the SynchroSpark Swarm (a mobile robot lab platform developed by us here at Monash), to study goal-to-goal motion planning. The core challenge is to coordinate a team of robots so that each vehicle safely reaches its assigned target position while avoiding collisions.

Our approach is to solve the problem centrally, broadcasting synchronized motion commands to each robot over Wi-Fi. This eliminates the need to burden each robot with heavy onboard computation.

The motion planner is formulated as a linear-quadratic (LQ) dynamic game. This sets up a coupled optimal control problem where each robot minimizes its own cost by balancing goal-tracking and collision avoidance, while simultaneously accounting for the behavior of the rest of the team. The game is solved via a centralized backward recursion based on coupled Riccati equations, yielding Nash equilibrium trajectories for the entire swarm.

The project covers the full pipeline from theory to hardware:

• Formulate the multi-robot system as a linear-quadratic dynamic game with distinct goal-tracking and collision-avoidance objectives.
• Implement a centralized solver adapted for differential-drive mobile robots to generate real-time motion commands.
• Integrate the planner with host-side tools and a Wi-Fi/MQTT command infrastructure.
• Evaluate the system on physical hardware, benchmarking performance against simpler baselines using metrics such as completion time, minimum inter-robot separation, and goal-reaching error.