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In this paper, we present an online motion planning algorithm (3D-OGSE) forgenerating smooth, collision-free trajectories over multiple planningiterations for 3-D agents operating in an unknown obstacle-cluttered 3-Denvironment. Our approach constructs a safe-region, termed 'generalized shape',at each planning iteration, which represents the obstacle-free region based onlocally-sensed environment information. A collision-free path is computed bysampling points in the generalized shape and is used to generate a smooth,time-parametrized trajectory by minimizing snap. The generated trajectories areconstrained to lie within the generalized shape, which ensures the agentmaneuvers in the locally obstacle-free space. As the agent reaches boundary of'sensing shape' in a planning iteration, a re-plan is triggered by recedinghorizon planning mechanism that also enables initialization of the nextplanning iteration. Theoretical guarantee of probabilistic completeness overthe entire environment and of completely collision-free trajectory generationis provided. We evaluate the proposed method in simulation on complex 3-Denvironments with varied obstacle-densities. We observe that each re-planingcomputation takes $\sim$1.4 milliseconds on a single thread of an Intel Corei5-8500 3.0 GHz CPU. In addition, our method is found to perform 4-10 timesfaster than several existing algorithms. In simulation over complex scenariossuch as narrow passages also we observe less conservative behavior.

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