Katarzyna Zadarnowska

Kinematic dexterity of mobile manipulators: an endogenous configuration space approach

A mobile manipulator is treated as a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator mounted on the platform. The kinematics of the mobile manipulator can be represented as a driftless control system with outputs. By adopting the endogenous configuration space approach we propose two kinematic dexterity measures, called local and global dexterity. The local dexterity, modeled upon the manipulability of stationary manipulators, indicates how infinitesimal motions in the configuration space propagate to the taskspace of the mobile manipulator. The global dexterity corresponds to L2-norm of the local dexterity over a prescribed region of the configuration space. Advantages of the endogenous dexterity measures over traditional performance measures of mobile manipulators known from the literature are described. Both the dexterities are employed for determining optimal configurations and optimal geometries of an exemplary mobile manipulator.

A control theory framework for performance evaluation of mobile manipulators

We propose a new, control theoretic methodology for defining performance measures of mobile manipulators. As a guiding principle, we assume that the kinematics or the dynamics of a mobile manipulator are represented by the end point map of a control system with outputs, and that a locally controllable system yields nontrivial performance measures. In the paper, we focus on two categories of dynamic performance measures: the compliance measure and the admittance measure. In both these categories, the following local and global performance characteristics are introduced: the agility ellipsoid, the agility and mobility, the condition number and the distortion. The usefulness of new local measures is demonstrated on the example of determining optimal motion patterns of a wheeled mobile robot.

Doubly nonholonomic mobile manipulators

We study doubly nonholonomic mobile manipulators composed of a nonholonomic mobile platform and a nonholonomic manipulator fixed to the platform. The kinematics of such mobile manipulators are represented by a pair of driftless control systems driven by platform and manipulator controls, and sharing an output function that describes positions and orientations of the end effector. The approach assumed in this paper is based on the concept of endogenous configuration defined as a pair of control functions of the platform, and of the aboard manipulator. For doubly nonholonomic mobile manipulators we define local performance measures and examine the inverse kinematic problem. Our results consist in a definition of the dexterity ellipsoid, a characterization of dextrous and isotropic endogenous configurations, and a derivation of a Jacobian pseudoinverse inverse kinematics algorithm. Computer simulations involving a 3 d.o.f. planar nonholonomic manipulator mounted on a kinematic car type platform illustrate our approach.

Task-Priority Motion Planning of Wheeled Mobile Robots Subject to Slipping

Wheeled mobile robots are most often assumed to be capable of rolling without slipping, and modeled as nonholonomic systems [3, 7, 19]. Such an assumption is far from realistic in practice. Since friction is the major mechanism for generating forces acting on the vehicle’s wheels, the problem of modeling and predicting tire friction has always been an area of intense research in the automotive industry [4, 13, 17]. Modeling friction forces exerted at the wheels has been used for various studies [1, 2, 10, 15].

Switched Modeling and Task---Priority Motion Planning of Wheeled Mobile Robots Subject to Slipping

This study is devoted to the modelling and control of Wheeled Mobile Robots moving with longitudinal and lateral slips of all wheels. Due to wheel slippage we have to deal with systems with changing dynamics. Wheeled Mobile Robots can be thus modeled as switched systems with both autonomous switches (due to wheel slippage) and smooth controls (due to control algorithm). It is assumed that the slipping is counteracted by the slip reaction forces acting at contact points of the wheels with the ground. A model of these reaction forces, borrowed from the theory of automotive systems, has been adopted and included into the Lagrangian dynamic equations of the robot. A framework for designing motion planning schemes devoid of chattering effects for systems with changing dynamics is presented. A task–priority motion planning problem for wheeled mobile robots subject to slipping is addressed and solved by means of Jacobian motion planning algorithm based on the Endogenous Configuration Space Approach. Performance of the algorithm is presented in simulations of the Pioneer 2DX mobile platform. The robot dynamics equations are derived and 4 variants of motion are distinguished. The motion planning problem is composed of two sub-tasks: robot has to reach a desired point in the task space (proper motion planning) and the motion should minimize either the control energy expendinture or the wheel slippage. Performance of the motion planning algorithm is illustrated by a sort of the parking maneuver problem.

Kinematic Motion Patterns of Mobile Manipulators

We address the problem of performance evaluation of mobile manipulators. It seems that this area has not been explored systematically in the literature; a list of representative references includes [6, 2, 7, 8, 1, 3].

Isotropic configurations of mobile manipulators

Abstract We consider the kinematics of a mobile manipulator composed of a nonholonomic mobile platform and a holonomic manipulator mounted on the platform. Velocity constraints imposed on the platform motion and the structure of the mobile manipulator taskspace translate naturally into a description of the kinematics by means of a driftless control system with outputs. An endogenous configuration of the mobile manipulator includes the control function of the platform and the joint position of the manipulator. We introduce the kinematic dexterity ellipsoid and study the isotropy of an endogenous configuration measured by its condition number. As an illustration, isotropic configurations are computed for an exemplary mobile manipulator built of a unicycle type platform with a double pendulum manipulator aboard.

Modeling and motion planning of wheeled mobile robots subject to slipping

We are studying the dynamics of wheeled mobile robots moving with longitudinal and lateral slips of all wheels. It is assumed that the slipping is counteracted by slip reaction forces acting at contact points of the wheels with the ground. A model of these reaction forces borrowed from the theory of automotive systems has been adopted, and included into the Lagrangian dynamic equations of the robot. In a control system representation of the dynamics the motion planning problem is addressed, and solved by means of the endogenous configuration space approach. A number of computer simulations involving the dynamics of the Pioneer 2DX mobile platform illustrate the performance of the motion planning algorithm.

Efficiency of Double Nonholonomic Mobile Manipulators

Abstract This paper deals with the problem of defining performance measures of doubly nonholonomic mobile manipulators composed of a nonholonomic mobile platform and a nonholonomic manipulator mounted on the platform. We introduce the kinematic theory of such mobile manipulators in frame of the endogenous configuration space approach, which assumes that: the kinematics of mobile manipulators is represented by a pair of driftless control systems driven by platform and manipulator controls, and sharing output function that describes position and orientation of the end-effector; the kinematic performance measures refer to the analytic Jacobian of the system; a locally controllable system yields nontrivial performance measures. Our results consist in a definition of the following local performance characteristics: the dexterity ellipsoid, the local dexterity, the energy efficiency and the motion efficiency. The usefulness of new local measures is demonstrated on the example of determining efficient configurations of a 3 d.o.f. planar nonholonomic manipulator fixed to a kinematic car type platform.