Janusz Jakubiak

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.

A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators

On the basis of a geometric characterization of repeatability we present a repeatable extended Jacobian inverse kinematics algorithm for mobile manipulators. The algorithms dynamics have linear invariant subspaces in the configuration space. A standard Ritz approximation of platform controls results in a band-limited version of this algorithm. Computer simulations involving an RTR manipulator mounted on a kinematic car-type mobile platform are used in order to illustrate repeatability and performance of the algorithm.

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.

Extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots

By a generalization of the well-known extended Jacobian method for stationary manipulators, we derive the extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots. Key points of the derivation consist in defining the kinematics of a mobile robot as the end-point map of a driftless control system, decomposing the space of control functions of this system into a finite and an infinite dimensional subspaces, and introducing an augmenting kinematics map subordinated to this decomposition. The original kinematics and the augmenting kinematics constitute the extended kinematics. The inverse Jacobian of the extended kinematics defines the extended Jacobian inverse kinematics algorithm. By design, the algorithm is repeatable. As an example, we derive a specific extended Jacobian inverse kinematics algorithm and illustrate its performance with the computer simulations.

A new geometric algorithm to generate smooth interpolating curves on Riemannian manifolds

This paper presents a new geometric algorithm to construct a C smooth spline curve that interpolates a given set of data (points and velocities) on a complete Riemannian manifold. Although based on a modification of the de Casteljau procedure, our algorithm is implemented in three steps only independently of the required degree of smoothness, and therefore introduces a significant reduction in complexity. The key role is played by the choice of an appropriate smoothing function which is defined as soon as the degree of smoothness is fixed.

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform-manipulator motion coordination.

ACCELERATION-DRIVEN KINEMATICS OF MOBILE MANIPULATORS: AN ENDOGENOUS CONFIGURATION SPACE APPROACH

Using the endogenous configuration space approach we study the inverse kinematic problem for mobile manipulators represented by an affine (not driftless) control system with outputs. A particular case of acceleration-driven mobile platform is addressed, and solved by means of a Jacobian pseudoinverse inverse kinematics algorithm. Performance of this algorithm has been illustrated with computer simulations involving the acceleration-driven kinematic car platform with RTR manipulator aboard.

Motion Planning of the Trident Snake Robot: An Endogenous Configuration Space Approach

We address the motion planning problem of the trident snake robot. The problem is solved with the help of the imbalanced Jacobian inverse kinematics algorithm dedicated to nonholonomic systems with constraints. Performance of the algorithm is illustrated with computer simulations.

Control of mobile robot for remote medical examination: Design concepts and users' feedback from experimental studies

In this article we discuss movement control of a ReMeDi medical mobile robot from the user perspective. The control is essentially limited to the level of operator actions where the operator is a member of a nursing staff. Two working modes are the base of considerations: long distance (LD) and short distance (SD) movement. In this context two robot control techniques are the subject of study: manual with use of a gamepad and “point and click” on a map that is related to autonomous motion with use of an onboard navigation system. In the SD mode the user manually operates the robot, that is close to a laying down patient on a settee. In the LD mode the mobile base moves autonomously in a space shared with people to the desired position. Two user studies were conducted. The results show that from the perspective of LD mode the autonomous navigation is efficient and reduces the burden of the medical personnel. In the SD case, the results show that the users were able to precisely position the robot. Besides, the users perceived the manual control with the gamepad as intuitive. In all cases the medical personnel consider this technology as safe and useful. Safety is also confirmed by patients.

Control and perception system for ReMeDi robot mobile platform

The paper presents a design of a control system of a mobile platform for a ReMeDi robotic system - a system for remote diagnosis with ultrasonography and palpation. The platform described in the paper is a first prototype of the mobile base for the system meant for evaluation of technical and user-defined requirements. We present the design of the platform, its control architecture and results of laboratory tests of platform localization methods and experiments how users perceive the robot made in a hospital.