A Set-based Motion Planning Algorithm for Aerial Vehicles in the Presence of Obstacles Exhibiting Hybrid Dynamics

This paper proposes a set-based motion planning algorithm to drive a quadrotor to a target location while avoiding multiple moving obstacles that have hybrid dynamics. By exploiting a library of motion primitives, the proposed planner is capable of rapidly generating trajectories that avoid obstacles with unknown angular velocities that instantaneously change at unknown impact times. The planner employs the reachable sets of the vehicle and of the obstacles to generate a set of safe trajectories from which a trajectory with lowest cost is selected. Simulations and experimental validation of the motion planner are presented.

I. Introduction

Small-scale aerial vehicles keep gaining popularity due to their versatility and wide range of applications. Nowa-days, these vehicles are used for search and rescue, fire monitoring, product delivery to just list a few. Their broad applicability has propelled research focusing on solving the motion planning problem with obstacle avoidance, leading to strategies ranging from velocity fields, which generates a vector field to drive the vehicle away from the obstacles and towards the goal [1], to graph search algorithms, which solve the motion planning problem using search algorithms [2]. A particularly popular approach is receding horizon control [3] [4], where the motion planning problem is recast into a constrained optimization problem. In this approach, the constrained optimization problem is recurrently solved over a receding horizon, using current measurements and predictions. Obstacle avoidance is achieved by imposing hard constraints within the optimization problem. In [5], a modular framework, called FaSTrack, is developed to enable motion planning that is fast, dynamically feasible, and safe in the presence of the static obstacles. In [6], a real-time motion planning framework with obstacle avoidance is proposed for quadrotors, but the dynamics of the obstacles are not considered. In [7], a set-based predictive control framework is proposed to optimize trajectories to safely guide a ground vehicle toward the target and predict dynamic obstacles that exhibit only continuous behavior. The motion of the dynamic obstacles is predicted using their discretized model. In [8], a nonlinear model predictive control approach is used to generate a series of safe control inputs for a quadrotor with obstacles that are classified to be static, linear, or projectile. The motion of obstacles is predicted using different continuous-time models depending on the type of obstacle.