A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form

Abstract

SUMMARYThis paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form.The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.

A survey of efficient computational methods for manipulator inverse dynamics

“…From the survey which has been presented in this paper, it is clear that the computational efficiency of an algorithm which solves the IDP can be made independent of [68] PUMA-600 304 212 Khosla and Newman [63] CMU DD Arm II 303 226 Kircanski et al [18] Stanford Arm 286 266 Newman and Murray [61] 'Stanford Arm 194 177 Khalil et al [64] Stanford Arm 187 152 Renaud [26] 6R simple robot 181 I27 Yang and Tzeng [70] A specially design robot 72 34…”

“…The reader interested in this topic can see the survey paper by Paul [15] or the more recent one by Newman and Murray [16] as well other papers dealing with specific applications [17][18][19][20]. Our goal in this paper is to present an up-to-date survey on various methods for deriving computationally efficient algorithms which solve the IDP for general rigid-link open-chain robot manipulators and can be implemented numerically on any conventional single-processor computer.…”

Real-time computational aspects of multiple manipulator systems

“…They minimize the program code and the execution time. There are several program packages that automatically generate customized symbolic models (see for example [9]), but there are also generalpurpose environments that can be used for the same purpose, like REDUCE, MATHEMATICA running either on PC's or mainframes. For example, the C file for computing position, orientation, and the hand Jacobian matrix generated by the SYM package [9,21] requires X(°T6,6 J)= 102 (2.6)…”

“…In the literature, the real-time computational complexity of the kinematic models [3,9,11,12,17,21], the dynamical models [2, 4, 6, 7, 9-12, 14, 16, 20, 22], and the control schemes [9,11,12,14] of single manipulator systems have been analyzed in great detail. There has been correspondingly little work in the same area for multiple manipulator systems.…”

Symbolic modeling in robotics: Genesis, applicaton, and future prospects

“…Basically it is aimed at generating various kinds of kinematic and dynamic robot models in SYMbolic form. It is a successor of SYMB evolved from an inverse dynamics symbolic model generator (1987, [35]) into a program environment which generates different kinds of models and performs a wide set of transformations on the generated models.…”