Object-Oriented Modeling and Control of Delta Robots

In this paper we derive a dynamic model of the Delta robot that is well-suited to an object-oriented modeling framework. The approach uses an augmented Lagrangian or Hamiltonian formulation together with Baumgarte's method of index reduction, and results in a singularity-free dynamic model that is well suited to dynamic analysis, control system synthesis and time-domain simulation. The object-oriented structure enables broad application to problems such as coordinated control and robotic assembly. We present several common control algorithms and conduct a dynamic analysis of the Delta robot that shows that the open-loop system is unstable for large volumes of the reachable workspace, which has fundamental implications on closed-loop performance.