Abstract-This paper proposes a computational method to solve constrained cooperative motion planning problems for multiple vehicles undergoing translational and rotational motions. The problem is solved by means of the Lie group projection operator approach, a recently developed optimization strategy for solving continuous-time optimal control problems on Lie groups. State constraints (for collision avoidance) are handled by means of a set of barrier functions, turning the optimization approach into an interior point method. A sample computation is shown to demonstrate the effectiveness of the method.
Motivated by increasingly complex and challenging missions at sea, there is widespread interest in the development of advanced systems for cooperative control of multiple autonomous marine vehicles. Central to the implementation of these systems is the availability of efficient algorithms for multiple vehicle path planning that can take explicitly into account the capabilities of each vehicle and existing environmental conditions. Examples include path planning to steer a group of marine vehicles and enable them to reach a specific target site simultaneously with a desired formation pattern, while avoiding inter-vehicle collisions, and online path replanning for a vehicle fleet upon detection of episodic events or obstacles.Multiple vehicle path planning methods build necessarily on key concepts and algorithms for single vehicle path following. However, they go one step further in that they must explicitly address such issues as inter-vehicle collision avoidance and simultaneous times of arrival. As such, they pose considerable challenges both from a theoretical and practical implementation standpoint.This paper is a brief survey of multiple vehicle path planning techniques. The exposition is focused on specific algorithms for path planning developed in the scope of research work in which the authors have participated. The algorithms make ample use of direct optimization methods that lead to efficient and fast techniques for path generation. The paper affords the reader a fast paced presentation of key algorithms that had their genesis in the aircraft field, discusses them critically, and suggests problems that warrant further consideration.
I. INTRODU CT IONThere is incre asing dem and for the use of autonomous mobile robots, which are steadily bec omin g the tools par excellen ce fo r the executi on of c halleng ing m issions in areas that are hard to acc ess or place hum an lives at risk. Space, land , and marine robot s are by now ubiquitous and hold promi se to the devel opment of networked systems to sample the envi ronment at an unp recedented sca le.Thi s trend is clea rly visible in the marin e world, which harb ors form idable challenges imposed by the extent of the areas to be surveye d, sea waves, curre nts, low visibility at , Vehic1e2 Fig. I. Multiple Vehicle Path Planning: Go-to-Formation Maneuver with Spatial Dcconflictiondepth, lack of global positioning sys tems unde rwater, and stringe nt aco ustic co mmunica tion co nstra ints. So me of these difficulties ca n be partially ove rco me through the use of fleets of heterogeneous vehicles workin g in coo peration, unde r the supervision of adva nced sys tems for cooperative co ntrol of multiple autonomous vehicles . Cent ral to the implementation of the se systems is the ava ilability of efficient algor ithms for mult iple vehicle path planning that ca n take explicitly into account the ca pabilities of each vehicle and existing envi ronm en tal co nditions.As an application exampl e, co nsider the scenario where multiple autonomo us marine vehicl...
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