Feedback Integrators for Nonholonomic Mechanical Systems
This work provides a numerical integration method for nonholonomic systems, which is important for robotics and mechanics, but the results are demonstrated on known examples without quantitative comparisons.
The authors extended feedback integrators to nonholonomic mechanical systems, preserving constraints and conserved quantities, and demonstrated the method on several examples including the Suslov problem and Chaplygin sleigh.
The theory of feedback integrators is extended to handle mechanical systems with nonholonomic constraints with or without symmetry, so as to produce numerical integrators that preserve the nonholonomic constraints as well as other conserved quantities. To extend the feedback integrators, we develop a suitable extension theory for nonholonomic systems, and also a corresponding reduction theory for systems with symmetry. It is then applied to various nonholonomic systems such as the Suslov problem on SO(3), the knife edge, the Chaplygin sleigh, the vertical rolling disk, the roller racer, the Heisenberg system, and the nonholonomic oscillator.