A sampling-based probabilistic path planner for multirotor air vehicles in cluttered environments

Abstract

Successful navigation of small, unmanned aerial vehicles (UAVs) in cluttered environments is a challenging task, especially in the presence of turbulent winds and state estimation uncertainty. This paper proposes a probabilistic path planner for UAVs operating in cluttered environments. Unlike previous sampling-based approaches which select robust paths from a set of trajectory candidates, the proposed algorithm seeks to modify an initial desired path so that it satisfies obstacle avoidance constraints. Given a desired path, Monte Carlo uncertainty propagation is performed and obstacle collision risks are quantified at discrete intervals along the trajectory. A numerical optimization algorithm is used to modify the flight path around obstacles and reduce probability of collision while maintaining as much of the originally desired path as possible. The proposed path planner is specifically designed to leverage embedded massively parallel computers for near real-time uncertainty propagation. Thus the planner can be run in real-time in a feedback manner, modifying the path appropriately as new measurements are obtained. Example results for a standard quadrotor show the ability of the path planning scheme to successfully generate trajectories in cluttered environments. Trade studies characterize algorithm performance as a function of obstacle density and collision risk acceptability.

Simulation and experimental results of an unmanned towed system

“…Along with the previously stated assumption of a rigid body structure, the rotor blades are considered to be fixed-pitch rotor blades perpendicular to the z axis of the driver's body frame and uses differential thrust and torque for control. 15,16 A schematic of a generic quadcopter can be seen in Figure 2. The total forces considered are the weight (F→W), thrust (F→t), aerodynamics (F→A), and tether line contact force (F→T).…”

“…The total forces considered are the weight (F→W), thrust (F→t), aerodynamics (F→A), and tether line contact force (F→T). Typically, rotor thrust is given by the equation below where the lumped parameter kt=CtρAR2 16

Figure 2.Quadcopter dynamic model.

…”

“…The aerodynamic contributions considered here is a combination of rotor blade flapping and induced drag. 16,28,29 With these aerodynamic contributions defined, the aerodynamic forces can be expressed as where dxD,dyD are the induced drag coefficients and A1s,A1c are positive constants that describe the rotor flapping response as a function of advancing ratio. The parameter η is a lumped parameter expressed as …”

“…The aerodynamic contributions considered here is a combination of rotor blade flapping and induced drag. 16,28,29 With these aerodynamic contributions defined, the aerodynamic forces can be expressed as…”

“…Kun and Hwang 15 used a multicopter dynamic model to create a linear matrix inequality-based adaptive controller. Rogers and Brown 16 used a similar nonlinear aerodynamic model to create a sampling-based probabilistic path planner for multicopter vehicles. Still further, Kose and Oktay 17 created multiple dynamic models of a quadcopter for different flight conditions.…”