A Time-Optimal Feedback Control for a Particular Case of the Game of Two Cars

Chaudhari, Aditya; Chakraborty, Debraj

doi:10.1109/tac.2021.3086300

Cited by 10 publications

(5 citation statements)

References 28 publications

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“…Note that the pursuer has different kinematic capabilities than in our case, where the pursuer is a DDR. That implies that the players' motion strategies found in [17], [26], [27] differ from those in our work. [18] also analyzes a pursuitevasion problem between two identical DDRs.…”

Section: Related Workcontrasting

confidence: 74%

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Capturing a Dubins Car With a Differential Drive Robot

Ruiz

2022

IEEE Access

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In this paper, we study the problem of capturing a Dubins Car with a Differential Drive Robot in minimum time. The two vehicles are represented like unitary discs moving in the plane without obstacles. Both agents have the same maximum speed and a bounded turning ratio. We frame the problem as a pursuit-evasion game. The Differential Drive Robot plays as a pursuer and aims to capture the Dubins Car as soon as possible. The Dubins Car, on the contrary, takes the evader's role and tries to avoid capture. Using differential game theory, we compute the players' time-optimal motion strategies to accomplish their tasks and provide analytical expressions describing them. In particular, we reveal four singular surfaces in this game. Two evader's dispersal surfaces (EDS) where the evader can choose between two controls and the pursuer must react accordingly, leading to trajectories with the same cost. One pursuer's dispersal surface (PDS) where the evader must select its control based on the pursuer's choice. And a transition surface (TS), where the DDR switches its controls. Some examples of the players' time-optimal motion strategies are shown in numerical simulations.

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Section: Related Workcontrasting

confidence: 74%

“…The authors found the timeoptimal motion strategies for both players. More recently, [26] presents a comprehensive solution to that problem, and [27] provides feedback-based solutions for particular cases. Note that the pursuer has different kinematic capabilities than in our case, where the pursuer is a DDR.…”

Section: Related Workmentioning

confidence: 99%

Capturing a Dubins Car With a Differential Drive Robot

Ruiz

2022

IEEE Access

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“…Again, given that the evader has different kinematic capabilities, the player's motion strategies found in [6] differ from the ones presented in the current work. A more comprehensive solution to the problem in [6] was presented in [14], and a feedback-based solution for particular cases is provided in [15]. However, since our evader is a DDR, our solution differs from those of [14] and [15].…”

Section: A Related Workmentioning

confidence: 99%

“…A more comprehensive solution to the problem in [6] was presented in [14], and a feedback-based solution for particular cases is provided in [15]. However, since our evader is a DDR, our solution differs from those of [14] and [15].…”

Section: A Related Workmentioning

confidence: 99%

Capturing a Differential Drive Robot With a Dubins Car

Ruiz

2023

IEEE Access

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This work addresses the pursuit-evasion problem of capturing a Differential Drive Robot (DDR) with a Dubins Car (DC) in minimum time. We model the problem as a zero-sum differential game, and using differential game theory, we compute the time-optimal motion strategies of the players near the end of the game. We unveil the existence of three singular surfaces: an Evader's Dispersal Surface (EDS), a Transition Surface (TS), where the DDR switches its controls, and a Pursuer's Universal Surface (PUS). A particular set of motion strategies for the players is used at each singular surface. To compute our solution, we assume that both players have the same maximum speed and a bounded turning ratio. Considering the previous setting, the game's outcome only depends on the particular motion capabilities of the players. From previous results in the literature and those presented in the current paper, we can establish that a DDR has an advantage when it plays as a pursuer or as an evader compared to a Dubins Car performing the same role.

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“…Du et al [9] report a deep learning framework using the Monte-Carlo method that achieves superior evasion metrics over random motion and spinning trajectories of the invader. The reachability state-space approach [10] is a relatively newer concept that has been found effective for local adaptations, often obtained by sacrificing optimality. Intelligent evasion policies based on prediction of the pursuer's motion is often termed as 'counter guidance', in reciprocation to the strategic navigation and guidance planning designed for pursuit vehicles.…”

Section: Introductionmentioning

confidence: 99%

Optimal Evasive Path Planning with Velocity Constraint

Biswas

Ghazzai

Kar

et al. 2022

2022 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

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Pursuit evasion is an important category of mobile robotics application related to surveillance, spying and gathering ambient information. This paper presents a novel optimal approach to evasion planning, considering physical limitations of the environment and the evader. The results show that the proposed formulation is applicable irrespective of the number of pursuing agents and the relative velocities of the pursuers and the evader, contrary to the traditional requirement that evasion strategies need to be configured according to situation-dependent cases. The proposed policy is generic and can be implemented in real-time by iterative optimization using model predictive controllers, the objective being avoidance of capture or at the least, maximizing the capture time.

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A Time-Optimal Feedback Control for a Particular Case of the Game of Two Cars

Cited by 10 publications

References 28 publications

Capturing a Dubins Car With a Differential Drive Robot

Capturing a Dubins Car With a Differential Drive Robot

Capturing a Differential Drive Robot With a Dubins Car

Optimal Evasive Path Planning with Velocity Constraint

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