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

Abstract

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.

Motion Planning in Urban Environments to Achieve Sensor Quality Metrics

“…The initial random dense tree (RDT) created for each simulation is based on the 3-D rapidlyexploring random tree (RRT) utilized in previous work 23 with some modifications made to the random node placement. The completely random node placement within the environment is now utilized 33.3% of the time.…”

“…The algorithm builds upon a trajectory planning strategy that was developed by implementing a simplified version of a Dubins car in 3-D and random dense trees with motion primitives. 23 This procedure considered expanding from an initial configuration along feasible trajectories, which are the motion primitives, to an expanding set of nodes that are chosen based on random dense tree growth. Those feasible trajectories are optimal between the nodes although the resulting trajectory has no guarantees of optimality for the entire path from the initial configuration to the final configuration.…”

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

“…This inclusion of the waypoint is critical for situations in which the time to climb to the desired altitude is greater than the time to travel to the desired North-East location. The simplest situation would have the vehicle climb or dive at maximum rate until reaching the desired altitude and then continue using a 2D solution until reaching the final configuration (Hurley et al 2009); however, that approach is infeasible when the rate of change of altitude is too small. The inability to move vertically for many aircraft requires the trajectory to add horizontal distance and provide sufficient time for the vehicle to change altitude.…”