An Inverse Differential Game Approach to Modelling Bird Mid-Air Collision Avoidance Behaviours

Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control

“…We now investigate our methods in a simulated twoplayer collision avoidance differential game closely related to the model proposed in [7] for the behaviours of birds in mid-air collision scenarios. Consider two players moving in three-dimensions and let Player i's position and velocity be q…”

“…Numerous problems in automatic control [1]- [4], economics [5], [6], and biology [7], [8] involve modelling and analysing interactions between players (or decision makers) in processes governed by differential equations. Techniques for finding the optimal controls (or decisions) of players in noncooperative differential games given their potentially conflicting objectives have therefore been well studied (cf.…”

“…[2]). The inverse problem of computing the objectives of players in noncooperative differential games from player controls has received considerably less attention [7], [9], [10]. In this paper, we propose two inverse noncooperative differential game methods and derive novel conditions under which they yield unique solutions.…”

“…There has been recent interest in generalising methods of discrete-time inverse dynamic games to the continuous-time setting with a focus on state dynamics governed by differential equations [7], [9], [10], [27]. These methods have primarily involved reducing the inverse differential game problem to inverse optimal control problems that can be solved with existing inverse optimal control techniques [9], [10].…”

“…For example, the bilevel methods of inverse optimal control of [28] and [29] have computationally expensive implementations that involve the solution of optimal control problems inside numeric optimisation routines. The bilevel and nested optimisation methods of inverse differential games proposed in in [7], [9] and derived from these bilevel methods of inverse optimal control thus also have computationally implementations that scale poorly with the number of players, and state and control dimensions. Similarly, the minimum principle method of inverse optimal control from [30] is unable to operate on trajectories with constrained controls, and so the minimum principle method of inverse differential games presented in [9] and [10] are also unable to handle constrained controls.…”