A Path-Parametrization Approach Using Trajectory Primitives for 3-Dimensional Motion Planning

Pachikara, Abraham; Kehoe, Joseph J.; Lind, Rick

doi:10.2514/6.2009-5625

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…The planning merely searches over the waypoint coordinates, C w 2 R 2 , for the optimization. In this case, each trajectory primitive that connects with the waypoint is computed from the closed-form algebraic solutions in a 2D plane and simply extended into 3D paths by introducing a climb rate through a similarity constraint (Pachikara et al 2009)…”

Section: Initial Trajectory Constrained To the Circle Helixmentioning

confidence: 99%

Path-Parameterization Approach Using Trajectory Primitives for Three-Dimensional Motion Planning

2013

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Motion planning determines trajectories for vehicles that link an initial location and heading with a final location and heading. Techniques for motion planning have been developed for two-dimensional maneuvering; however, they are less mature for three-dimensional maneuvering. The concept of motion primitives is particularly attractive for motion planning that determines trajectories as a set of maneuvers that satisfy differential constraints. This paper furthers work on a higher-level abstraction of trajectory primitives that consider sequences of motion primitives. In this paper, trajectory primitives are developed that deal with airspace constraints of an environment. The motion planning is shown to be an optimization involving a pair of trajectory primitives that is related by an intermediate waypoint. The resulting path is completely parameterized by the waypoint location.

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Section: Initial Trajectory Constrained To the Circle Helixmentioning

confidence: 99%

Path-Parameterization Approach Using Trajectory Primitives for Three-Dimensional Motion Planning

2013

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“…Such an approach does not generate feasible solutions for all configurations that require more time for vertical translation than horizontal translation; however, techniques are developed that introduce waypoints to optimize the path and allow sufficient time to increase vertical translation. 24 Even so, the current constraint is actually not restrictive since a set of intermediate configurations are chosen to satisfy the assumptions on time to travel using the approach for motion planning in this paper.…”

Section: B Motion Planningmentioning

confidence: 99%

A Mixed Local-Global Solution to Motion Planning within 3-D Environments

Lind

Kehoe

2009

AIAA Guidance, Navigation, and Control Conference

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Autonomous flight through urban environments requires methods to generate trajectories that traverse a region and its associated obstacles. This paper introduces the development of a 3-dimensional motion planning algorithm using a random dense tree whose branches are motion primitives from a 3-dimensional version of the Dubins car called the Dubins airplane. The motion primitives consist of 3-dimensional maneuvers formulated as combinations of turn segments and straight segments with an associated constant rate of climb. The resulting motion planner builds the tree by pruning nodes that intersect 3-dimensional obstacles while connecting the remaining nodes with the motion primitives. An example demonstrates the motion planner can avoid building-style obstacles and even bridges using feasible paths that are sub-optimal solutions to minimize the cost of flight time.

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“…As a result, researchers began to find other models to get some paths which are easier to be calculated but might be longer than the shortest path. In some papers such as [1,[7][8][9][10][11][12][13][14][15][16][17][18], the authors considered some approaches to get the final path. One of the advantages of such approaches is that it could be used in the environments with some obstacles only after a little bit changes.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, when considering the Dubins problem with obstacles, the original result will no longer be suitable, because the Dubins path might pass through the obstacles so the result needs to be changed a little. For 3D cases, the approaches used in [8][9][10][11][12][13][14][15][16][17] can be used only by a little change, because the result is not the shortest paths in either condition. It is a pity that we cannot get the shortest path with obstacles in 3D cases.…”

Section: Introductionmentioning

confidence: 99%

2D Dubins Path in Environments with Obstacle

Yang

Sun

2013

Mathematical Problems in Engineering

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We recapitulate the achievement about the Dubins path as well as some precise proofs which are important but omitted by Dubins. Then we prove that the shortest path (R*-geodesic) in environments with an obstacle consists of no more than five segments, each of which is either an arc or a straight line. To obtain suchR*-geodesic, an effective algorithm is presented followed by a numerical simulation as verification.

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A Path-Parametrization Approach Using Trajectory Primitives for 3-Dimensional Motion Planning

Cited by 7 publications

References 10 publications

Path-Parameterization Approach Using Trajectory Primitives for Three-Dimensional Motion Planning

Path-Parameterization Approach Using Trajectory Primitives for Three-Dimensional Motion Planning

A Mixed Local-Global Solution to Motion Planning within 3-D Environments

2D Dubins Path in Environments with Obstacle

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