###### Abstract  
NURBS curve parameter interpolation is extensively employed in precision trajectory tasks for industrial robots due to its smoother performance compared to traditional linear or circular interpolation methods. The trajectory planning systems for industrial robots necessitate four essential functional modules: first, the spline curve discretization technique ensuring chord error compliance; second, the contour scanning technique for determining the maximum feasible feed rate for multi-constraint and multi-segment paths; third, the technique for achieving a smooth feed rate profile; and fourth, the continuous curve parameter interpolation technique. Therefore, this paper proposes a high-precision planar NURBS interpolation system for industrial robots. Firstly, a segmentation method for NURBS curves based on a closed-loop chord error constraint is proposed, which segments the original global NURBS curve into a collection of Bezier curves that strictly meet the chord error constraint. Secondly, a bidirectional scanning technique is presented to meet the joint space constraint, establishing an analytical mapping between the tool tip kinematic constraint and the joint kinematic constraint. Then, based on the traditional S-shaped feed rate profile, an adaptive algorithm with a displacement constraint is introduced, considering the real-time speed adjustment requirements of robots. Finally, a compensation interpolation strategy based on arc length parameterization is adopted to solve the accumulated error problem in parameter interpolation. The effectiveness of and potential for enhancing the quality of planar machining of the proposed planar NURBS interpolation system for industrial robots are validated through simulations and experiments. The results demonstrate the system's applicability and accuracy, and its ability to improve planar machining quality. NURBS; parameter interpolation; industrial robot; closed-loop chord error constraint; S-shaped feed rate profile; bidirectional scanning Article  
A High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot  
[PERSON]; [PERSON] A High-Precision Planar NURBS Interpolation System Based on Method  
[PERSON]. the research on high-precision trajectory planning and interpolation systems for industrial robots is of great significance. In order to achieve high-speed and high-precision machining, many scholars have devoted themselves to studying techniques such as parameter curve segmentation, feed speed contour adjustment, and parameter curve interpolation. Traditional flat paths typically use a large number of short line segments instead of the entire curve, which inevitably leads to discontinuous tangent directions and abrupt changes in curvature, resulting in a decrease in feed rate. Due to the lack of G1 and G2 continuity at the junctions of adjacent line segments, rate fluctuations and changes in acceleration often occur. Nonuniform rational B-spline (NURBS) parameter curves have effectively addressed the above problems [3] and have become the standard format for free-form curves and surfaces. Based on the above issues, the current mainstream research content on planning and interpolation systems can be divided into three aspects. Firstly, there is the estimation method for NURBS path chord error. Currently, the majority of studies utilize curvature threshold segmentation techniques, which belong to open-loop chord error control and cannot ensure that real-time curve interpolation meets the chord error requirements throughout the entire machining process. Although there have been some studies [4; 5; 6] on accurately calculating chord error, the calculations are quite complex, so approximate estimation methods such as the second-order penetration circle method [7] are commonly used. [PERSON] et al. [8] proposed a B-spline approximation scheme method with tool tip position adjustment. NURBS is divided into several subdivisions according to the discrete curvature.