  Controlling complex tasks in robotic systems, such as circular motion for
cleaning or following curvy lines, can be dealt with using nonlinear vector
fields. In this paper, we introduce a novel approach called rotational obstacle
avoidance method (ROAM) for adapting the initial dynamics when the workspace is
partially occluded by obstacles. ROAM presents a closed-form solution that
effectively avoids star-shaped obstacles in spaces of arbitrary dimensions by
rotating the initial dynamics towards the tangent space. The algorithm enables
navigation within obstacle hulls and can be customized to actively move away
from surfaces, while guaranteeing the presence of only a single saddle point on
the boundary of each obstacle. We introduce a sequence of mappings to extend
the approach for general nonlinear dynamics. Moreover, ROAM extends its
capabilities to handle multi-obstacle environments and provides the ability to
constrain dynamics within a safe tube. By utilizing weighted vector-tree
summation, we successfully navigate around general concave obstacles
represented as a tree-of-stars. Through experimental evaluation, ROAM
demonstrates superior performance in terms of minimizing occurrences of local
minima and maintaining similarity to the initial dynamics, outperforming
existing approaches in multi-obstacle simulations. The proposed method is
highly reactive, owing to its simplicity, and can be applied effectively in
dynamic environments. This was demonstrated during the collision-free
navigation of a 7 degree-of-freedom robot arm around dynamic obstacles
