Cubic Bézier shaping impact angle constrained guidance for intercepting maneuvering targets

This paper presents a cubic Bézier shaping approach (CBSA) guidance strategy for solving the impact-angle-constrained interception problem against maneuvering targets under acceleration saturation. The Bézier shaping guidance strategy is formulated under the two-dimensional space engagement model by strategically configuring four control points in the cubic Bézier parameterization. This approach generates smooth spatial trajectories that simultaneously guide the interceptor to intercept maneuvering targets while satisfying terminal constraints. The CBSA guidance strategy strategically determines four control points, defined by the initial position, desired terminal point, and Bézier parameters through quantitative analysis, to shape the spatial trajectory. This parameterization directly governs the curve’s smoothness, curvature profile, and arc length, ensuring simultaneous achievement of precise target interception and ideal impact angle. Thus, the boundary of the Bézier parameter space is analyzed under the traditional Bézier curve, and the optimal control point configuration is determined. Based on simulation outcomes, the proposed CBSA guidance strategy not only meets the impact angle constraint but also delivers high interception accuracy. In comparison with quadratic BSA and piecewise BSA approaches, it exhibits notable improvements in computational efficiency and overall guidance performance.