Motion planning for multiple non-holonomic robots: a geometric approach

Xidias, Elias K.; Aspragathos, Nikos Α.

doi:10.1017/s0263574707003980

Cited by 12 publications

(5 citation statements)

References 25 publications

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“…Multi-robot optimal motion planning is even more computationally challenging, because the worst-case computational complexity exponentially grows as the robot number. Current multi-robot motion planning mainly falls into three categories: centralized planning [5] [6], decoupled planning [7] [8] and priority planning [9] [10]. Noticeably, none of these multirobot motion planners are able to guarantee the optimality of returned solutions.…”

Section: Introductionmentioning

confidence: 99%

Pareto optimal multi-robot motion planning

Zhao

Zhu

2018

2018 Annual American Control Conference (ACC)

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This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to identify the Pareto optimal solutions where no robot can unilaterally reduce its traveling time without extending others'. The consistent approximation of the algorithm in the epigraphical profile sense is guaranteed using set-valued numerical analysis. Real-world experiments and computer simulations show the anytime property of the proposed algorithm; i.e., it is able to quickly return a feasible control policy that safely steers the robots to their goal regions and it keeps improving policy optimality if more time is given.1 Throughout this paper, product order is imposed; i.e. two vectors a, b ∈ R N are said "a is less than b in the Pareto sense", denoted by a b, if and only if a i ≤ b i , ∀i ∈ {1, · · · , N }. Similarly, strict inequality can be defined by a ≺ b ⇐⇒ a i < b i , ∀i ∈ {1, · · · , N }.

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Section: Introductionmentioning

confidence: 99%

Pareto optimal multi-robot motion planning

Zhao

Zhu

2018

2018 Annual American Control Conference (ACC)

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“…Jiang et al 10 presented an optimal motion planning strategy that generates minimum-time, first-derivative-smooth paths for a mobile robot. Finally, Xidias and Aspragathos 26 developed a geometrical approach for generating simultaneously optimal smooth paths for a set of non-holonomic robots.…”

Section: Introductionmentioning

confidence: 99%

Novel three-dimensional optimal path planning method for vehicles with constrained pitch and yaw

2016

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SUMMARYThis paper presents a novel method for generating three-dimensional optimal trajectories for a vehicle or body that moves forward at a constant speed and steers in both horizontal and vertical directions. The vehicle's dynamics limit the body-frame pitch and yaw rates; additionally, the climb and decent angles of the vehicle are also bounded. Given the above constraints, the path planning problem is solved geometrically by building upon the two-dimensional Dubins curves and then Pontryagin's Maximum Principle is used to validate that the proposed solution lies within the family of candidate time-optimal trajectories. Finally, given the severe boundedness constraints on the vertical motion of the system, the robustness of the proposed path planning method is validated by naturally extending it to remain applicable to high-altitude final configurations.

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“…Regarding the multi-robot open-loop motion planning, the approaches mainly fall into three categories: centralized planning in; e.g., [24], [28], decoupled planning in; e.g., [15], [26] and priority planning in; e.g., [9], [12]. Centralized planning is complete but computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

Game theoretic controller synthesis for multi-robot motion planning Part I: Trajectory based algorithms

Zhu

Otte

Chaudhari

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number.

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Motion planning for multiple non-holonomic robots: a geometric approach

Cited by 12 publications

References 25 publications

Pareto optimal multi-robot motion planning

Pareto optimal multi-robot motion planning

Novel three-dimensional optimal path planning method for vehicles with constrained pitch and yaw

Game theoretic controller synthesis for multi-robot motion planning Part I: Trajectory based algorithms

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