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Physical systems are classified into linear and nonlinear ones. Nonlinear systems can be further divided into holonomic and nonholonomic systems. Holonomy and nonholonomy are key concepts for such classification and describes the essential difference of behaviors of physical systems. In this section, definitions and several examples of the holonomic and the nonholonomic systems are presented.
Recently the nonholonomic mechanical systems have received much attention in the field of robotics and control engineering. Nonholonomic systems are typically controllable in a configuration space of higher dimension than the input space. Therefore, behaviors of the nonholonomic systems are often found to be rich, even if there are a few control inputs. Previous works on the nonholonomic...
Since a nonholonomic manipulator was theoretically designed from the viewpoint of kinematic constraints and nonlinear control, mechanical implementation and prototyping are significant in practice. Since joint actuating torques are transmitted through the nonholonomic gears using frictional forces, a prototype should be carefully designed to assure the principle of velocity transmission,...
Nonholonomic underactuated systems are typically modelled as highly nonlinear ones, which becomes obvious as the dimension of the system increases. To the author’s knowledge, so far there is no canonical form for the general nonholonomic systems, for example, free flying space robots. Therefore, even a proof of the controllability is made based on numerical computations, for example, see...
Since the chained form manipulator has a well-conditioned kinematic model, development of efficient control strategy for the chained form directly contributes to the improvement of actual performances in practice. In section 3.5, several control strategies were shown and verified with the prototype of the nonholonomic manipulator.
Controllable underactuated manipulators were successfully developed based on the nonlinear control theoretic approach. The nonholonomic gear is designed to create nonlinear structure on the robot manipulator. The nonholonomic gear is a special type of velocity transmission consisting of a ball and wheels, and provides the kinematic nonholonomic constraint. The gear can be employed not only...
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