Efficient Simulation and Analysis of Complex Rigid Body Dynamic Systems Subject to Unilateral Constraints

Rensselaer Polytechnic Institute, Troy NY

Investigators

Abstract

This research is associated with the extension of recently developed RCR and ODCA dynamics simulation and analysis algorithms to deal with complex articulated multibody systems involving both bilateral and unilateral constraints in the context of complementarity theory. The proposed method differs markedly from more traditional approaches in how constraints are treated and the associated complementarity problem is formed for an articulated body system. Specifically, the proposed formulation effectively decomposes the mass matrix and directly embeds the constraints within the equations of motion as they are being formed. The methods thereby removes the costs associated with producing the system mass and constraint Jacobian matrices, as well as their subsequent decompositions, and additionally decouples the unilateral (inequality) constraint loads from much of the other analysis. Thus, the resulting equations should enforce the constraints at a very small fraction of the cost usually associated with formulating, manipulating and solving the system motion, and constraint equations within a complementarity problem. Systems possessing mU unilateral constraints face a 2mU possibility combinatorial problem, for which a consistent solution may not exist. The combinatorial search, generally needed to obtain a consistent solution, may be eliminated (or at least drastically reduced) through the satisfaction of the equations of motion simultaneously with the unilateral constraints complementarity conditions (i.e. Signorini's law) using approaches such as Lemke's method. The performance of the developed method will be compared with that obtained in modeling and simulation the identical systems using a more traditional complementarity approaches. The issue of problem solution uniqueness and physical correctness will also be rigorously investigated.