Trajectory-planning through interpolation by overlapping cubic arcs and cubic splines

• Published in: International journal for numerical methods in engineering Vol. 57; no. 11; pp. 1615 - 1641
• Main Authors: du Plessis, L. J., Snyman, J. A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 21.07.2003
• Subjects: Acceleration; Automation; cubic spline interpolation; Interpolation; machine tool orientation; Machine tools; Mathematical analysis; Methodology; non-uniform rational B-splines (NURBS); Orientation; overlapping cubic arcs; planar industrial robot; Splines; trajectory-planning
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.739

A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end‐effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time‐domain. Further user‐specified information is used to determine how the end‐effector orientation angle should vary along the specified curve. The proposed trajectory‐planning methodology is embodied in a computer‐algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time‐domain. If a varying end‐effector orientation angle is specified, the OCAS‐algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time‐domain. The trajectory‐planning capabilities of the OCAS‐algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non‐linear functions, as well as for nodal points specified along a non‐analytical (free‐form) test‐curve. The proposed trajectory‐planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free‐form curves. Copyright © 2003 John Wiley & Sons, Ltd.