<p>The discontinuity of tangent, curvature, and curvature derivative of the 5-axis toolpath consisting of line and arc segments defined by the G01/G02/G03 commands limits the performance of hybrid robot in high-efficiency and high-precision milling machining. To guarantee the high-order continuous and smooth machining, a C³ continuous corner smoothing 5-axis toolpath containing spatial arc segments is semi-analytically generated. Firstly, the control points of the smoothing quintic B-spline for line and arc segments are constructed analytically based on the G³ continuity conditions. Within the constraints of the established explicit smoothing error expressions, the G³ continuous smoothing for three kinds of tooltip positions, namely, spatial line-line pairs, arc-arc pairs, and line-arc pairs, is investigated. Meanwhile, the smoothing error model of tool orientation is analytically established. Then, the parameter synchronization of the tool orientation at the junction following the tooltip position is achieved by replacing the remaining segments with seven B-spline curves as synchronization curves. Finally, simulations and experiments with the typical 5-axis toolpath containing spatial arc segments are carried out to verify the validity of the proposed method in ensuring C³ continuous motion in the robot operation space and good following performance in the joint space.</p>