Modeling closed loop mechanisms is a necessity for the control and simulation of various systems like parallel robots, series-parallel hybrid robots, linkages, musculoskeletal systems etc. and pose a great challenge to rigid body dynamics algorithms. Many commercial software (e.g. ADAMS, RecurDyn, Simmechanics, V-Rep etc) and a very limited number of rigid body dynamics libraries (e.g. RBDL [2], DARTS [3], OpenSim [4,5]) pro vides this support. Solving the equations of motion for rigid body system with closed loops require resolution of loop closure constraints which are often solved via numerical rocedures. This brings additional burden to these algorithms as they have to stabilize and control the loop closure errors additionally. In order to circumvent this issue, in recent work [1], a kinematics and dynamics library called Hybrid Robot Dynamics (HyRo-Dyn) is proposed, which provides a modular and analytical framework for resolving loop closure constraints in highly complex series-parallel hybrid robots. At the moment, HyRoDyn only allows the analytical resolution of loop closure constraints for the parallel mechanisms that are known to its database.

The next step is to extend the software so that it can deal with loop closure constraints numerically for arbitrary mechanisms in a modular way. Numerical resolution of loop closure constraints are well known in the literature but a hybrid of analytical and numerical approach for solving loop constraints is missing in the literature. This thesis will implement the state of the art numerical loop closure techniques (e.g. cut joint or cut body) in rigid body dynamics in a modular way in HyRoDyn which will not only enhance the generality and applicability of this software tool but also provide insights into the trade-o between the modelling eort and generality of a multi-body simulation software. The work done in this thesis will be applied to the modelling and control of a complex biologically inspired series-parallel humanoid (RH5) or Recupera exoskeleton system mous Rough Terrain Excavator Robot (ARTER).