Ole Jakob Sørdalen

Conversion of the kinematics of a car with n trailers into a chained form

The authors propose a set of coordinates for the kinematics model of a car with n trailers with only two degrees of freedom. The absolute position of the system is given by the location of the rear trailer. By using these coordinates, the kinematic model is locally converted into a nilpotent, chained form. Control strategies for chained systems can be applied to locally control a car with n trailers.<<ETX>>

Exponential control law for a mobile robot: extension to path following

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. >

A multisteering trailer system: conversion into chained form using dynamic feedback

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.

Control properties of underactuated vehicles

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.

Design of a nonholonomic manipulator

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.<<ETX>>

Feedback control of a nonholonomic underwater vehicle with a constant desired configuration

In this article we present a feedback control law that gives exponential convergence of a nonholonomic underwater vehicle to a constant desired configuration. This is achieved using a piecewise smooth feedback control law that is based on previous work on the control of nonholonomic mobile robots in the plane. The kinematic model of the underwater vehicle is given in SE(3) by homogeneous transformation matrices, and attitude deviations are given by Euler parameters. This gives a global description without singularities. It is also shown how controllability of the nonholonomic underwater vehicle can be analyzed in SE(3) without the use of local charts. The inputs of the system are the three angular velocity components and the forward velocity.

Exponential stabilization of a car with n trailers

It is shown how a class of two-input nonholonomic systems can be converted into a chained form. This is used to convert a car with n trailers into a chained form. The position of the system is given by the location of the last trailer. A time-varying feedback control law for the stabilization of a chained form with exponential convergence to the origin is presented. A coordinate transformation and input feedback transformation is derived to obtain asymptotic stability with exponential convergence to any desired configuration, locally in the orientations of the trailers. Simulation results are presented for a car with three trailers.<<ETX>>

Exponential stabilization of a nonholonomic underwater vehicle with constant desired configuration

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.<<ETX>>

Prototyping a nonholonomic manipulator

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.

A multi-steering trailer system: Conversion into chained form using dynamic feedback

In this paper, we examine in detail the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, connected together with rigid bars. We define the state space and kinematic equations of the system, modeling the pair of wheels on each axle as able to roll but not slip. we then investigate how this system of kinematic equations may be converted into multi-input 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. In order to convert the system to this multi-input chained form, we use dynamic state feedback. We draw some motivation from the very simple example of a kinematic unicycle and the relationships of the angular velocities therein, and we show how the dynamic state feedback that we use corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. We briefly discuss how some of the methods which have been proposed for steering and stabilizing two-input chained form systems can be generalized to multi-chained systems. for concreteness, we also present two different example systems: a fire truck (three axles) and a five-axle, two-steering system. Simulation results for a parallel-parking maneuver for the five-axle system are included in the form of margin movies.