Todd Murphey
The aerospace corporation
| Reduction theory has been extensively studied for smooth mechanical systems. However, nonsmooth mechanical systems have not received as much attention in this context. In particular, many systems can potentially have more nominal constraints (both holonomic and nonholonomic) than they have degrees of freedom, thereby ensuring that at least some of these constraints cannot be satisfied. In some cases, particularly those involving friction, determining which constraints are satisfied can be very difficult and sensitive to uncertainty in the model. For instance, the Mars rover is a vehicle equipped with six independently driven wheels, two of which are independently steered. Partially because of this high degree of articulation, it has sufficiently many nonholonomic constraints that the only motion which satisfies all of its constraints is the straight forward motion. Once the wheels are turned, some wheels must slip. At the same time, we can expect the Mars rover to share characteristics with the kinematic car studied frequently in the nonlinear control community. Properties such as controllability as well as motion planning and stabilization techniques are well established for the kinematic car, and we would like them to be useful for the rover as well. We have been developing tools for the purpose of analysis and control design for overconstrained systems (such as the Mars rover and some MEMS problems). I will give an overview of our recent results regarding necessary and sufficient condition for kinematic reducibility for nonsmooth mechanical systems. I will then discuss how this can be used for controllability, motion planning, and stabilization analysis in the context of a few examples. |
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