Depth Map based Guidance Law of Quadrotor System for Obstacle Shape Mapping and Reactive Collision Avoidance

Abstract

Diverse research topics on Unmanned Aerial Vehicles (UAVs) have emerged as the UAV has received great attention due to lots of advantages. Among its numerous applications, shape mapping is an important means of collecting information of an unknown environment. As the UAV has been used as a platform in the shape mapping, an appropriate path must be generated to efficiently map an object. Furthermore, to successfully perform missions including the shape mapping, the UAV must have the ability to detect and avoid obstacles of various shapes using the obstacle information acquired by an onboard sensor. This is critical because a collision with these obstacles may result in fatal damage and potentially mission failure. In this dissertation, a guidance law for obstacle shape mapping and reactive collision avoidance is proposed. A quadrotor dynamic model is constructed, and a control system is designed based on the feedback linearization and linear quadratic tracker techniques. A stereo vision system with a limited field of view and sensing range is assumed to be mounted on the quadrotor to obtain obstacle information by utilizing a depth map. For shape mapping, the states of the quadrotor are used to generate a path for appropriate obstacle mapping in real time. The quadrotor moves around the obstacle to map the overall shape of the obstacle while avoiding collisions. The quadrotor performs horizontal and vertical maneuvers if the image plane of the vision system cannot cover the entire obstacle. The horizontal and vertical maneuvers are performed in sequence to develop a systematic scheme to efficiently map the obstacle. For collision avoidance, an ellipsoid is chosen as a circumscribed bounding box to contain the acquired obstacle data points, which can be obtained by solving a convex optimization problem. An affine transformation is used to form a collision cone consisting of straight lines tangent to the ellipsoid. A collision condition is examined using the collision cone and velocity vector of the quadrotor. A hierarchical clustering method is proposed to deal with multiple obstacles, and the bounding boxes are updated using the clusters. Numerical simulations including a Monte Carlo simulation are performed to demonstrate the performance of the proposed shape mapping and collision avoidance algorithms.