Keywords: automatic code generation, inverse dynamic model, parallel robot system, computed torque control.

Serial robot systems are limited in the achievable accelerations due to the weight of the axis drives, which are moved during the manipulator activity. In certain applications parallel robot systems can increase the acceptable accelerations while preserving the wanted accuracy at the cost of reduced workspace, because a full parallel robot system has all drives mounted on the rigid base platform. Choosing advanced composite fibre materials, which have a very good stiffness to weight ratio, the acceleration limit can be raised further. But such systems need accurate models of their kinematic and dynamic behaviour in order to fully understand their flexibility and degrees of freedom. Additionally unwanted structural vibrations are more likely and can be controlled by smart structural control schemes [1]. Such structural control algorithms typically are combined with linearized system models, which are obtained by system identification in the workspace, but for simulation purposes model based linearized models are advantageous in order to predict the achievable structural damping.

General purpose multi-body systems such as SIMPACK or ADAMS are very useful tools for common tasks and for verification purposes, but in practice it is often advantageous to have direct access to the underlying system equations as well as to the implemented data flow in the equations. For the trajectory controlled robot control, rigid body models are needed to obtain the kinematic and dynamic equations. The kinematic equations are essential for the correct implementation of the robot task. To reduce the deviation of the actual trajectory path with respect to the planned one, inverse dynamic models are successfully used in the so-called computed torque control algorithm [2].

This paper suggests a hierarchical software architecture to allow a compact formulation of the underlying equations in a matrix/tensor orientated way. This method has been successfully used for a general purpose kinematic modul to solve the direct (DKP) and inverse (IKP) kinematical problem for simulation and display purposes. Further on real-time capable inverse dynamic models of the HEXA and the TRIGLIDE structure have been automatically set up from a formulation in a tensor based high level scripting language to facilitate a computed torque control on these machines. Other investigations currently being considered belong to overconstrained substructures and calculation of approximative forces in these components as well as extracting elastic linearized models for structural control from the dynamic equations, which are enriched by additional stiffness and friction items.

The software hierarchy is established using three layers. The upper layer describes the problem in an application oriented simple descriptive form. The middle layer is a matrix/tensor based scripting language currently implemented in PERL. The bottom layer consists of a very fast symbolic processor, which optimizes the equation tree of elementary terms with some sophisticated stragegies, producing the final C-code to be finally incorporated in the real-time environment or in simulation environments like MATLAB.

1

S. Algermissen, R. Keimer, M. Rose, E. Breitbach, H.P. Monner, "Applied robust control for vibration suppression in parallel robots", in Proceedings of 22nd International Symposium on Automation and Robotics in Construction (ISARC), Ferrara, Italy, September 2005.

2

J. Hesselbach, C. Budde, J. Maaß, E. Breitbach, M. Rose, "Dynamic performance enhancement of a hexa-parallel-robot using the computed torque approach", Proceedings of Mechatronics & Robotics, pp. 1006-1011, 2004.

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