A differential game theoretic approach for two-agent collision avoidance with travel limitations

This work presents a collision avoidance control strategy that solves the Hamilton-Jacobi-Isaacs (HJI) equation for an agent to quickly take action assuming a worst-case scenario. By doing so, the agent can develop a control strategy that is robust to the strategies of other agents with whom collision is possible. Consequently, if the governing dynamics of the agent are sufficient, then a collision can be avoided. We build on the idea of finding control solutions by using a differential game theoretic approach (Mettenheim and Breitner, 2009). This is beneficial because the opposing agent's strategy is incorporated into the control by assuming it plays the worst-case actions. The approach in this work solves the zero-sum aspects of the control on-line using a fast solution method that operates over partitions in the state space (Goode et al.; ASME J Dyn Syst Meas Control, 2011). We form the solution to the Homicidal Chauffeur game which is used to provide the control for an evader attempting to avoid a pursuer, an agent that deviates from its normal path and into that of the evader. Furthermore, the evader is constrained to remain within defined boundaries of its assigned travel area, such as a road lane, water channel, etc. The control strategy consists of three parts: (1) a zero-sum approximation of collision avoidance, (2) high-level path planning, and (3) low-level vehicle control. Each component is explained, and an example is given using a real robotic vehicle control system. Here, we show how the control can be implemented using a simple processor located on a vehicle that seeks to avoid a collision with another oncoming vehicle, making a left turn.