A new Maple toolchain for generating rigid body dynamics in symbolic form for robot manipulators is presented. The peculiarity compared to existing tools lies in the framework of Bash scripts controlling the full workflow of the toolchain with a high degree of automation. The optimized Matlab code generated by Maple is automatically converted to function files with proper documentation and input assertions. This renders manual post-processing of the results unnecessarily. The focus of the paper is on the implemented unit-testing framework according to the method of test-driven development. By providing the test framework together with the generated code in a stand-alone version, a good test coverage and a good software quality can be achieved. The results of the open source project provide a basis for dynamics simulations for robot dimensional synthesis or in model-based control of robot manipulators in research or in industrial context. The general software approach can be applied to other fields where theoretical models are derived with Maple.
Geometric formulations for the inverse kinematics problem (IKP) in robotics are often set up in the full Cartesian space of three translational and three rotational coordinates (3T3R). When transferring this to tasks with spatial rotation like 3T2R, 2T3R or 2T2R, the result is usually not defined in a minimal set of independent coordinates. Removing the excluded operational space coordinates completely from the expressions is interesting from a theoretical point of view and simplifies further calculations. This can be achieved by formulating a 2R residual using the Z-Y -X Tait-Bryan angles and a 2T residual derived by the projection of the pointing direction on a plane. In this paper, the minimal-coordinate IKP is derived for 2T2R and 2T3R tasks on position level with application to a gradient-projection scheme. Limitations of the redundant coordinate are considered within the nullspace.
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