Multi-vehicle path planning in dynamically changing environments

Ahmadzadeh, Ali; Motee, Nader; Jadbabaie, Ali; Pappas, George J.

doi:10.1109/robot.2009.5152520

Cited by 19 publications

(20 citation statements)

References 13 publications

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“…The main feature of the proposed algorithm in Table I is that it initiates the search for an optimal solution from small penalties and increases them incrementally until the duality gap is zero. In the following section, we show that there is an interesting connection between the alternative dual formulation and elastic multi-particle systems [28].…”

Section: Theoremmentioning

confidence: 90%

“…We can impose curvature constraint onχ by imposing some norm constraints on the vertices [28]. If we assume that l 1 κ max , then we can impose the discrete curvature constraint κ i ≤ κ max through the following norm constraints on the vertices…”

Section: Task Planning For Multiple Vehiclesmentioning

confidence: 99%

“…Thus, the dual function (16) is the minimum potential energy of all springs which is parameterized by the magnitude of spring-like forces µ, λ, and γ. In [28], it is shown that if the magnitude of the spring-like forces are chosen appropriately, then the set of all stable equilibria of the dynamical systems (19) is equal to the set of all feasible solutions of nonconvex optimization problem (15). In the following theorem, e ij = Theorem 2: Consider the multi-particle dynamical system (19) with net force…”

Section: A Dynamical System Interpretation Of Alternative Dualitymentioning

confidence: 99%

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A duality approach to path planning for multiple robots

Motee

Jadbabaie

Pappas

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-In this paper, we propose an optimization-based framework for path planning for multiple robots in presence of obstacles. The objective is to find multiple fixed length paths for multiple robots that satisfy the following constraints: (i) bounded curvature, (ii) obstacle avoidance, (iii) and collision avoidance. First, we formulate a relaxation of the path planning problem using polygonal approximations. We show that path planning problem for multiple robots under various constraints and missions, such as curvature and obstacle avoidance constraints as well as rendezvous and maximal total area coverage, can be cast as a nonconvex optimization problem. Then, we propose an alternative dual formulation that results in no duality gap. We show that the alternative dual function can be interpreted as minimum potential energy of a multiparticle system with discontinuous spring-like forces. Finally, we show that using the proposed duality-based framework, an approximation of the minimal length path planning problem (also known as Dubins' problem) in presence of obstacles can be solved efficiently using primal-dual interior-point methods.

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Section: Theoremmentioning

confidence: 90%

Section: Task Planning For Multiple Vehiclesmentioning

confidence: 99%

Section: A Dynamical System Interpretation Of Alternative Dualitymentioning

confidence: 99%

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A duality approach to path planning for multiple robots

Motee

Jadbabaie

Pappas

2010

2010 IEEE International Conference on Robotics and Automation

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“…Constrained multi agents architectures for dynamic planning of many variants of PDP were proposed [10], [11], [12], [13], [14]. Here agents search cooperatively an optimal plan satisfying a predefined set of constraints distributed over them.…”

Section: Carrier Agentmentioning

confidence: 99%

A Multi Agent Based Organizational Architecture for Dynamic Pickup and Delivery Problem

Guerram

2018

CIT

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Pickup and Delivery Problem (PDP) consists of searching an optimal set of vehicles and an optimal set of routes, one route by each vehicle, in order to pickup items from a set of origins and deliver them to another set of destinations. Pickup and delivery problem is a class of complex systems whose complexity is NP Hard. In PDP real life applications, heuristics and meta heuristics methods are used in order to obtain an acceptable solution in reasonable execution time. When unpredictable events, like for example path cut and vehicles failure, may occur during the PDP schedule execution, we say that the PDP is dynamic (DPDP) and in this case we have to revise this schedule. In this paper, we propose a multi agent architecture for DPDP based on an organizational architecture. Supported by a formal framework, the proposed architecture allows us to show, through a case study that computed solution for the studied problem could be done in a parallel manner which attenuates substantially the problem complexity. ACM CCS (2012) Classification

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“…A trajectory planning approach in multi-vehicle and dynamic environment (e.g. moving obstacles) which is also based on numerical optimization is provided in [1]. SIPP [27] is a path (trajectory) planning method for environments with moving obstacles.…”

Section: Related Workmentioning

confidence: 99%

Towards a Trajectory Planning Concept: Augmenting Path Planning Methods by Considering Speed Limit Constraints

Chrpa

Osborne

2013

J Intell Robot Syst

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Trajectory planning is an essential part of systems controlling autonomous entities such as vehicles or robots. It requires not only finding spatial curves but also that dynamic properties of the vehicles (such as speed limits for certain maneuvers) must be followed. In this paper, we present an approach for augmenting existing path planning methods to support basic dynamic constraints, concretely speed limit constraints. We apply this approach to the well known A* and state-of-the-art Theta* and Lazy Theta* path planning algorithms. We use a concept of trajectory planning based on a modular architecture in which spatial and dynamic parts can be easily implemented. This concept allows dynamic aspects to be processed during planning. Existing systems based on a similar concept usually add dynamics (velocity) into spatial curves in a post-processing step which might be inappropriate when the curves do not follow the dynamics. Many existing trajectory planning approaches, especially in mobile robotics, encode dynamic aspects directly in the representation (e.g. in the form of regular lattices) which requires a precise knowledge of the environmental and dynamic properties of particular autonomous entities making designing and implementing such trajectory planning approaches quite difficult. The concept of trajectory planning we implemented might not be as precise but the modular architecture makes the design and implementation easier because we can use (modified) well known path planning methods and define models of dynamics of autonomous entities separately. This seems to be appropriate for simulations used in feasibility studies for some complex autonomous systems or in computer games etc. Our basic implementation of the augmented A*, Theta* and Lazy Theta* algorithms is also experimentally evaluated. We compare i) the augmented and basic A*, Theta* and Lazy Theta* algorithms and ii) optimizing of augmented Theta* and Lazy Theta* for distance (the trajectory length) and duration (time needed to move through the trajectory).

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Multi-vehicle path planning in dynamically changing environments

Cited by 19 publications

References 13 publications

A duality approach to path planning for multiple robots

A duality approach to path planning for multiple robots

A Multi Agent Based Organizational Architecture for Dynamic Pickup and Delivery Problem

Towards a Trajectory Planning Concept: Augmenting Path Planning Methods by Considering Speed Limit Constraints

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