Nonholonomic constraints are exploited to design a controllable n-joint manipulator with only two inputs. Gears subject to nonholonomic constraints are designed to transmit velocities from the inputs to the passive joints. The system possesses a triangular structure for which a conversion into chained form is presented. The nonholonomic manipulator can, therefore, be controlled with an open loop or a closed loop using existing controllers for chained form. Mechanical design is established, and experimental results proved the usefulness of design of the nonholonomic manipulator and applied control schemes. While previous publications have assumed that the nonholonomic systems are given and have developed theory for these systems, this paper points out a new direction where the nonholonomic theory is used to design controllable and stabilizable systems.

We proposed a nonholonomic manipulator which is a controllable n joints manipulator with only two inputs, exploiting a special kind of velocity transmission called a nonholonomic gear. Since the nonholonomic manipulator was theoretically designed from the viewpoint of kinematic constraints and nonlinear control, the mechanical implementation and prototyping are extremely important in practice. In this paper, the principle of mechanical design of a nonholonomic manipulator is established, and the experimental results are shown using a prototype nonholonomic manipulator.

This paper studies control properties of the dynamics of underactuated vehicles (e.g. underactuated surface vessels, underwater vehicles, aeroplanes or spacecraft). The unactuated dynamics implies constraints on the accelerations. Both the necessary and sufficient conditions for these constraints to be second-order nonholonomic, first-order nonholonomic or holonomic are developed. It is shown that underactuated vehicles with a gravitational field where the elements corresponding to the unactuated dynamics are zero, are not C/sup 1/ asymptotically stabilizable to a single equilibrium.

This paper examines the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, linked together with rigid bars. The state space and kinematic equations of the system are defined, and it is shown how these kinematic equations may be converted into a multiinput chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization; some of these methods are discussed here. Dynamic state feedback is used to convert the system to this multiinput chained form. It is shown how the dynamic state feedback that is used in this paper corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. Two different example systems are also presented, along with simulation results for a parallel-parking maneuver.

Presents a feedback control law which gives exponential stabilization of a nonholonomic underwater vehicle to a constant desired configuration. This is achieved by transforming the kinematic model into a chained form, and applying a control scheme for exponential stabilization of chained form systems. The nonholonomic vehicle under consideration is described by a kinematic model with three angular velocities and one translational velocity component as inputs. The kinematic model of the underwater vehicle is given in SE(3) by a position vector and a rotation matrix. Due to the difference in topology, the transformation into chained form is not global, but has singularities for large angular deviations. This problem is discussed, and conditions for avoiding the singularities are derived.>

Nonholonomic systems are typically controllable in a configuration space of higher dimension than the input space. Here, it is shown how nonholonomic constraints can be exploited to design a controllable n-joint manipulator with only two inputs. Gears subject to nonholonomic constraints are designed to transmit velocities from the inputs to the unactuated joints. The designed nonholonomic manipulator is shown to be completely controllable in the whole configuration space. The system is designed with a triangular structure for which a conversion into chained form is presented. The nonholonomic manipulator can, therefore, be controlled using existing controllers for chained form.>

A piecewise smooth feedback control law for path following for the kinematic model of a nonholonomic mobile robot is proposed. The resulting motion can consist of stopping and reversing phases. The desired path is supposed to be composed of straight lines and arcs of circles joined at intermediate configurations. The proposed feedback control law yields exponential convergence to configurations representing stopping phases and to the terminal configuration.>

The authors present an exponentially stable controller for a two-degree-of-freedom robot with nonholonomic constraints. Although this system is controllable, it has been shown to be nonstabilizable via smooth state feedback. A particular class of piecewise continuous controller which exponentially stabilizes the robot about the origin was previously proposed by the authors (1991). This approach is extended to stabilize about an arbitrary position and orientation, and to track a sequence of points. This feedback law is naturally combined with path planning when the desired path to be followed can be composed of a sequence of straight lines and circle segments, i.e. shortest paths of bounded curvature in the plane.>