3D-OGSE: Online Smooth Trajectory Generation for Quadrotors using Generalized Shape Expansion in Unknown 3D Environments

In this letter, we present an online motion planning algorithm for generating smooth, collision-free trajectories for quadrotors operating in an unknown, cluttered 3D environment. Our approach constructs a non-convex safe-region termed generalized shape at each timestep, which represents the obstacle-free region in the environment. A collision-free path is computed by sampling points in the generalized shape and is used to generate a smooth, time-parameterized trajectory by minimizing snap. The generated trajectories are constrained to lie within a convex subset of the generalized shape, which ensures the quadrotor maneuvers in the local obstacle-free space. This process is repeated at each timestep to re-plan trajectories until the quadrotor reaches its goal position. We evaluate the proposed method in simulation on complex 3D environments with high obstacle densities. We observe that each re-planing computation takes $\sim1.6$ milliseconds on a single thread of an Intel Core i5-8500 3.0 GHz CPU. In addition, our method is 6-10x faster than prior online motion planning methods, and we observe less conservative behavior in complex scenarios such as narrow passages.