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An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically uses iteration techniques. A difficulty with iteration schemes is that convergence becomes increasingly difficult under increasingly heavy loads. Here we devise a numerical scheme that does not involve iteration. Instead, a linear problem is solved at every time step. The scheme is fully automatic, stable and efficient. We illustrate this technique by solving a relaxation test in which a rigid spherical indenter is brought rapidly into normal contact with a thick elastic substrate lubricated by a liquid film. The sphere is then fixed in position as the pressure relaxes. We also carried out relaxation experiments on a lubricated soft PDMS (polydimethysiloxane) substrate under different conditions. These experiments are in excellent agreement with the numerical solution.
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Tuning-Free Contact-Implicit Trajectory Optimization
We present a contact-implicit trajectory optimization framework that can plan contact-interaction trajectories for different robot architectures and tasks using a trivial initial guess and without requiring any parameter tuning. This is achieved by using a relaxed contact model along with an automatic penalty adjustment loop for suppressing the relaxation. Moreover, the structure of the problem enables us to exploit the contact information implied by the use of relaxation in the previous iteration, such that the solution is explicitly improved with little computational overhead. We test the proposed approach in simulation experiments for non-prehensile manipulation using a 7-DOF arm and a mobile robot and for planar locomotion using a humanoid-like robot in zero gravity. The results demonstrate that our method provides an out-of-the-box solution with good performance for a wide range of applications.
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- Award ID(s):
- 1928654
- PAR ID:
- 10194660
- Date Published:
- Journal Name:
- IEEE International Conference on Robotics and Automation
- ISSN:
- 1049-3492
- Page Range / eLocation ID:
- 1183-1189
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
