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

Abstract

SUMMARYA 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-e ector of the mechanism. Given these speciÿed points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are ÿtted in the Cartesian domain and a cubic Spline interpolation curve is ÿtted in the time-domain. Further user-speciÿed information is used to determine how the end-e ector orientation angle should vary along the speciÿed 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-e ector orientation angle is speciÿed, 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 deÿned by analytically known non-linear functions, as well as for nodal points speciÿed 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.

An optimally re-configurable planar Gough–Stewart machining platform

“…13 are specified. The rest of the inputs for the OCAS trajectory-planning algorithm [11] are the same as specified for parabolic tool path no. 1 (see Section 5.1.1), which results in the Table 4 Parabolic tool path no.…”

“…8, together with a maximum allowable tangential acceleration along the tool path of 0.01 m/s 2 , and a required tangential cutting speed of 1 m/min % 0.0167 m/s are the specified inputs for the OCAS trajectory-planning algorithm [11]. With these specifications, the simulated prescribed motion is completed in 29.46 s. It is also required that the moving platform of the test-model be tangentially orientated with respect to the prescribed Cartesian curve resulting in the moving …”

“…First, given the prescribed tool path, the Overlapping Cubic Arcs and cubic Splines (OCAS) interpolating trajectory-planning algorithm [11] is used to find time dependent cubic splines for the three degree of freedom (DOF) motion of the moving platform (body 1 in Fig. 2).…”

Trajectory planning for industrial robot using genetic algorithms

“…On the other hand, the search takes place in the system's state space in the direct approaches. These approaches involve optimal control and numerical optimization (see Saramago and Steffen 2001, Plessis and Snyman 2003, Gasparetto and Zanotto 2007.…”

“…For depth knowledge you should refer to Piazzi and Visioli 1997a, Saramago and Steffen 2001, Plessis and Snyman 2003, Behzadipour and Khajepour 2006, Valero et al 2006, Bertolazzi et al 2007, Gasparetto and Zanotto 2007 A characteristic of indirect methods is that the path is known previously; either because it depends on the activity to be done by the industrial robot or because it has been generated by a path planner. Generally speaking, the indirect methods combine the path planning with the obtaining of the time history of motion usually in a sequential way.…”