Solving nonconvex problems of multibody dynamics with contact and small friction by successive convex relaxation.
Time-stepping methods using impulse-velocity approaches are guaranteed to have a solution for any friction coefficient, but they may have nonconvex solution sets. We present an example of a configuration with a nonconvex solution set for any nonzero value of the friction coefficient. We construct an iterative algorithm that solves convex subproblems and that is guaranteed, for sufficiently small friction coefficients, to retrieve, at a linear convergence rate, the velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled. In addition, we show that one step of the iterative algorithm provides an excellent approximation to the velocity solution of the original, possibly nonconvex, problem if the product between the friction coefficient and the slip velocity is small.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- NSF; SC; OUS
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 961233
- Report Number(s):
- ANL/MCS/JA-45649
- Journal Information:
- Mech. Des. Struct. Mach., Journal Name: Mech. Des. Struct. Mach. Journal Issue: 3 ; 2003 Vol. 31
- Country of Publication:
- United States
- Language:
- ENGLISH
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