Rotatingturning

Rotatingturning is a motion primitive used in robotics and automated control to describe a maneuver that combines rotation about the vehicle’s center with a turning motion, producing both a change in orientation and a translation in a single continuous action. It is used to model trajectories where turning and heading adjustment occur together rather than in separate steps.

Mathematically, a rotatingturning can be described for a planar robot with pose (x, y, θ). The standard nonholonomic bicycle or differential-drive kinematics give dx/dt = v cos θ, dy/dt = v sin θ, dθ/dt = ω, where v is the forward speed and ω is the angular rate. A rotatingturning specifies a finite window of time over which v and ω are nonzero, yielding a net rotation Δθ and a curved displacement (Δx, Δy). The resulting path depends on the curvature κ = ω/v (when v ≠ 0) and on the chosen velocity profile, enabling a smooth transition from initial to final pose without intermediate rewrite of the trajectory.

Applications span planetary robotics, warehouse automation, autonomous vehicles, and any system requiring smooth, compact maneuvers. Rotatingturning can simplify path planning by replacing separate turn and straight segments with a single blended action, reducing control overhead and potentially improving energy efficiency and execution smoothness.

Key considerations include nonholonomic constraints, actuator limits, and state estimation accuracy. While advantageous for producing continuous trajectories, rotatingturning may be constrained by wheel slippage, dynamic feasibility, and sensor latency. See also motion primitives, SE(2) representations, and arc or clothoid trajectories.