  In constrained solution spaces with a huge number of homotopy classes,
stand-alone sampling-based kinodynamic planners suffer low efficiency in
convergence. Local optimization is integrated to alleviate this problem. In
this paper, we propose to thrive the trajectory tree growing by optimizing the
tree in the forms of deformation units, and each unit contains one tree node
and all the edges connecting it. The deformation proceeds both spatially and
temporally by optimizing the node state and edge time durations efficiently.
The unit only changes the tree locally yet improves the overall quality of a
corresponding sub-tree. Further, variants to deform different tree parts
considering the computation burden and optimizing level are studied and
compared, all showing much faster convergence. The proposed deformation is
compatible with different RRT-based kinodynamic planning methods, and numerical
experiments show that integrating the spatio-temporal deformation greatly
accelerates the convergence and outperforms the spatial-only deformation.
