Singularities of the robotic arm DAE. (English) Zbl 1471.70007
Reis, Timo (ed.) et al., Progress in differential-algebraic equations II. Proceedings of the 9th workshop on descriptor systems, Paderborn, Germany, March 17–20, 2019. Cham: Springer. Differ.-Algebr. Equ. Forum, 433-480 (2020).
Summary: One of the benchmarks for higher-index DAEs is the so-called robotic arm, which results from a tracking problem in robotics. Testing this benchmark, we became aware of the singularities that appear and started to analyze them thoroughly. To our knowledge, there is no comprehensive description of the singularities appearing in this example in the DAE literature so far. For our analysis, we use different methodologies, which are elaborated in this article. This detailed inspection results from two different index concepts, namely the projector based analysis of the derivative array and the direct projector based DAE analysis associated with the tractability index. As a result, with both approaches we identify the same kinds of singularities. Some of them are obvious, but others are unexpected.
For the entire collection see [Zbl 1445.34004].
For the entire collection see [Zbl 1445.34004].
MSC:
| 70E60 | Robot dynamics and control of rigid bodies |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L80 | Numerical methods for differential-algebraic equations |
| 93C85 | Automated systems (robots, etc.) in control theory |
Keywords:
robotic arm problem; singularity; differential-algebraic equation; DAE; projector based analysis; derivative array; differentiation index; tractability indexReferences:
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