  In this paper, we present an online motion planning algorithm (3D-OGSE) for
generating smooth, collision-free trajectories over multiple planning
iterations for 3-D agents operating in an unknown obstacle-cluttered 3-D
environment. Our approach constructs a safe-region, termed 'generalized shape',
at each planning iteration, which represents the obstacle-free region based on
locally-sensed environment information. A collision-free path is computed by
sampling points in the generalized shape and is used to generate a smooth,
time-parametrized trajectory by minimizing snap. The generated trajectories are
constrained to lie within the generalized shape, which ensures the agent
maneuvers in the locally obstacle-free space. As the agent reaches boundary of
'sensing shape' in a planning iteration, a re-plan is triggered by receding
horizon planning mechanism that also enables initialization of the next
planning iteration. Theoretical guarantee of probabilistic completeness over
the entire environment and of completely collision-free trajectory generation
is provided. We evaluate the proposed method in simulation on complex 3-D
environments with varied obstacle-densities. We observe that each re-planing
computation takes $\sim$1.4 milliseconds on a single thread of an Intel Core
i5-8500 3.0 GHz CPU. In addition, our method is found to perform 4-10 times
faster than several existing algorithms. In simulation over complex scenarios
such as narrow passages also we observe less conservative behavior.
