A hybrid numerical and analytical approach towards resolving loop closure constraints in rigid body dynamics

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 poses 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, OpenSim [4, 5]) provides 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 procedures. This brings an 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 (HyRoDyn) is proposed, which provides a modular and analytical framework for resolving loop closure constraints in highly complex series-parallel hybrid robots. HyRoDyn only allows the analytical resolution of loop closure constraints for the parallel mechanisms that are known to its database.
The work done in the thesis extends the generality of the software significantly as it deals with the loop closure constraints numerically in a modular way. The user can choose to solve a submechanism numerically in the HyRoDyn software by providing the loop constraints in a YAML Ain’t Markup Language (YAML) file. The software architecture involves parsing of loop closure constraints defined by the user and a new class is implemented to handle them numerically. A case study of the hybrid series-parallel robot is performed for validation and results.The thesis also studies a recursive forward dynamics algorithm for closed loop systems [3]. The work done in this thesis can be applied to the modeling and control of a complex biologically inspired series-parallel hybrid robots when the analytical resolutions of loop closures is not available.