Safe Attitude Corridor: A Convex Optimization Method for Tool Orientation Smoothing in Five-Axis CNC Machining

When employing five-axis machine tools for freeform surface machining, feasible domains that ensure collision-free tool movement often manifest as concave regions and/or disconnected subdomains. Planning smooth tool orientation within such feasible domains while respecting geometric and kinematic constraints is a significant challenge. This article introduces a novel planning framework to improve the tool orientation smoothness in five-axis machining, based on the concept of safe attitude corridor (SAC). Our proposed SACs define regular, collision-free regions shaped as convex polyhedra within the feasible domains, transforming irregular, nonconvex feasible domains into convex constraints succinctly represented by linear inequalities. This convexification not only ensures strict adherence to the collision-free requirement (i.e., the geometric constraint) but also expedites the subsequent tool orientation optimization process. Utilizing the continuous quintic B-spline curve representation of rotary axis motions, kinematic indicators are expressed in B-spline forms, enabling the effective management of kinematic constraints by bounding the linear combinations of control points. By integrating the within-SAC constraints and the linearized kinematic constraints, our method formulates the tool orientation smoothing as a quadratic programming problem that minimizes the integral of squared jerk in the rotary axis motion. Simulations and laboratory experiments are given for validation purposes.