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A Differential Game Theoretic Approach for Two-Agent Collision Avoidance with Travel Limitations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 136 Durham Hall, Blacksburg, VA, 24061, USA

    Brian J. Goode

  2. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 7 Randolph Hall, Blacksburg, VA, 24061, USA

    Michael J. Roan

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  1. Brian J. Goode
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  2. Michael J. Roan
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Correspondence to Brian J. Goode.

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Authors sponsored by ONR Contract No. N00014-06-1-0356

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Goode, B.J., Roan, M.J. A Differential Game Theoretic Approach for Two-Agent Collision Avoidance with Travel Limitations. J Intell Robot Syst 67, 201–218 (2012). https://doi.org/10.1007/s10846-012-9657-x

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  • DOI: https://doi.org/10.1007/s10846-012-9657-x

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