Reachable Set for a drone

Quadcopters are increasingly popular for robotics applications. Being able to efficiently calculate the set of positions reachable by a quadcopter within a time budget enables collision avoidance and pursuit-evasion strategies.

This research computes the set of positions reachable by a quadcopter within a specified time limit using a simplified 2D model for quadcopter dynamics. This popular model is used to determine the set of candidate optimal control sequences to build the full 3D reachable set at final time T in (x,z,θ) phase space or rotated to form the set in (x,y,z) Cartesian space. We calculate the analytic equations that exactly bound the set of positions reachable in a given time horizon for all initial conditions. We use these bounds to: escape a bounded region, avoid a collision, find the collision set, determine the closest point to the reachable set, reach a goal (x,z) in the reachable set, and for drone countermeasures.