Modeling of rigid-link and compliant joint manipulator using the discrete body dynamics method

Recently, there has been a growing interest in robots with compliant elements. The commonly used methods for modeling their dynamics are multibody dynamics (MBD), recursive algorithms, impulse-based, and Lagrangian formulation. However, the latter method requires a new derivation for each change made to the system, and modeling compliant elements with it can be challenging. To solve complex systems that include compliant elements, a numerical method is necessary. Whereas some methods provide accurate solutions but have high complexity (e.g., MBD), others are quick but inaccurate (e.g., impulse-based). In this paper, we propose a new method, discrete body dynamics (DBD), which offers quick solutions with high accuracy, especially for systems with compliant elements. The method uses springs and dampers to model joints instead of constraints such as a revolute joint and has a complexity of O(n). We demonstrate the proposed method using single- and three-link manipulators with compliant joints and compare the results to those of ADAMS (a commercial MBD-based program) and the Lagrangian formulation. Our results show that the DBD method well matches with the Lagrangian formulation and is more accurate than the MBD for both compliant and rigid joints.