The connection between geometry and mechanics goes back a long way perhaps even as far back as Archimedes. In the 19th century, at the height of the industrial revolution, many of the prominent mathematicians of the day, Chebyshev, Darboux and Sylvester to name just a few, were studying the geometry of mechanisms and machines. Some of the foundations of modern geometry date back to this period, although it is difficult to tell this from a reading of modern texts in geometry. For most of the 20th century, however, this connection was largely ignored by mathematicians and engineers. But the past few years have seen an increasing number of mathematicians looking at geometrical problems in robotics. A few of them have published their work in robotics journals but most have been content to publish their work in maths journals or at specialised conferences. This special issue of Robotica seeks to expose some of this work to a more general robotics audience and begin a mutually beneficial discussion between the mathematicians, computer scientists and engineers. The idea is to present some of the more advanced material in this area to demonstrate to the wider robotics community the power, range and sophistication of these modern ideas. It is hoped that this special issue will show that modern mathematical techniques have a great deal to offer for the practising engineers. Also that many problems in engineering can give rise to interesting and sophisticated mathematics.

This paper develops a controller for position tracking of a new ball wheel drive mechanism for a robust omnidirectional wheeled mobile platform, an adaptive controller with physical parameter estimation. This platform, integrated with a manipulator, is designed for use in highway maintenance and construction, which is a generally unstructured and congested environment. The proposed ball wheel mechanism can move in all directions on the plane, instantaneously and isotropically. Reconfiguration of the redundant drive system of the ball wheel mechanism is accomplished by altering the contact pressure between the drive wheels and the sphere based on platform heading direction. The system redundancy is resolved through a Weighted Optimal Torque Distribution method allowing for smooth reconfiguration. Finally, experimental and simulation results demonstrate the effectiveness of the approach.

This paper deals with the stability of null-space velocity control algorithms in extended operational space for redundant robots. We compare the performance of the control algorithm based on the minimal null-space projection and generalized-inverse-based projection into the Jacobian null-space. We show how the null-space projection affects the performance of the null-space tracking algorithm. The results are verified with the simulation and real implementation on a redundant mobile robot composed of 3 degrees of freedom (DOFs) mobile platform and 7-DOF robot arm.

This paper presents a simple methodology for the quantitative and qualitative analysis of the performance of spherical parallel platforms. The quaternion formulation is used to represent the possible rotations, showing the workspace as a three-dimensional (3-D) solid object. The singularities of the platform intersect graphically with its workspace, allowing a graphical study of the mechanism kinematics. The performance criterion considered here has been the local dexterity of the manipulator. This methodology has been used to study and analyze three known orientation parallel platforms: 3-RRR, 3-UPU-wrist, and 2-UPS-1-RU. The objective of this study is to analyze the ability of these platforms to be utilized as mechanisms for the neck and shoulders of humanoid robots. Finally, the forces on actuators in some typical motions for neck and shoulder are plotted.

The idea underlying this Special Issue arises from previous successfully international events organized in this robotics context. Thus, during 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, hosted in Edmonton, Canada, a Workshop, with the same title was successfully organized by this guest editor. Moreover, this editor was involved in this research area, as co-Chair of the “Manipulation and Grasping Interest Group”, within the European Robotics Research Network (i.e. EURON), from 2001, organizing also a couple of International Summer Schools, supported by EURON, on these topics (Spain, 2001 and 2004). On the other hand, as time goes by, more and more robotics applications are oriented towards working in all kind of service domains, such as hospitals, museums, etc. Hence, the interest on those robotic systems, integrating manipulation and navigation capabilities, namely mobile manipulators, is drastically increasing around the entire world. Therefore, this special issue is trying to face this new scenario providing a comprehensive overview of some key topics, foundations and applications within the Mobile Manipulators context, including human-robot interaction aspects and critical issues related with navigation and manipulation performance, among others.

In this research, we study the construction of configuration space (C-space) of manipulators. The proposed approach is based upon precomputing the global topology of a robot's free space, and consists of an offline phase and an online phase. In the offline phase, a C-space obstacle database (COD) for a given robot is developed in which the C-space obstacle (C-obstacle) maps are stored and indexed by the cells of the workspace; in the online phase when the same robot is operated in a real environment, those maps whose indices match the real obstacle cells are identified and then extracted from the COD. The superposition of these maps forms forbidden region in operation. This proposed approach is a generic one and can be applied to manipulators with arbitrary kinematic structures and geometries. The construction of the COD, which is generally the most time-consuming step, is implemented in the offline phase, and the online computing only involves the identification of the components matching the COD indices. Therefore, this proposed approach for C-space construction can be realized in a real-time online fashion and is especially suitable for robot manipulation under dynamic operations. We carry out analyses on several types of manipulators to verify and demonstrate the feasibility and efficiency of the proposed approach.

We consider the task-oriented modeling of the differential kinematics of nonholonomic mobile manipulators (NMMs). A suitable NMM Jacobian is defined that relates the available input commands to the time derivative of the task variables, and can be used to formulate and solve kinematic control problems. When the NMM is redundant with respect to the given task, we provide an extension of two well-known redundancy resolution methods for fixed-base manipulators (Projected Gradient and Task Priority) and introduce a novel technique (Task Sequencing) aimed at improving performance, e.g., avoiding singularities. The proposed methods are applied then to the specific case of image-based visual servoing, where the NMM image Jacobian combines the interaction matrix and the kinematic model of the mobile manipulator. Comparative numerical results are presented for two case studies.

An understanding of how humans and robots can successfully interact to accomplish specific tasks is crucial in creating more sophisticated robots that may eventually become an integral part of human societies. A social robot needs to be able to learn the preferences and capabilities of the people with whom it interacts so that it can adapt its behaviors for more efficient and friendly interaction. Advances in human– computer interaction technologies have been widely used in improving human–robot interaction (HRI). It is now possible to interact with robots via natural communication means such as speech. In this paper, an innovative approach for HRI via voice-controllable intelligent user interfaces is described. The design and implementation of such interfaces are described. The traditional approaches for human–robot user interface design are explained and the advantages of the proposed approach are presented. The designed intelligent user interface, which learns user preferences and capabilities in time, can be controlled with voice. The system was successfully implemented and tested on a Pioneer 3-AT mobile robot. 20 participants, who were assessed on spatial reasoning ability, directed the robot in spatial navigation tasks to evaluate the effectiveness of the voice control in HRI. Time to complete the task, number of steps, and errors were collected. Results indicated that spatial reasoning ability and voice-control were reliable predictors of efficiency of robot teleoperation. 75% of the subjects with high spatial reasoning ability preferred using voice-control over manual control. The effect of spatial reasoning ability in teleoperation with voice-control was lower compared to that of manual control.

This investigation presents locomotion control of a hydraulically actuated six-legged humanitarian demining robot by robust adaptive fuzzy control in conjunction with the dead zone compensation technique within independent joint control framework. For proper locomotion of the demining robot, accurate tracking of the desired joint trajectory is very important. However, high degree of nonlinearity, the uncertainties due to changing hydraulic properties, and delay due to the flow of oil and dead zone of the proportional electromagnetic control valve results into an inaccurate plant model for the hydraulically actuated robotic joints. Consequently, model-based classical control techniques result into a large tracking error. Therefore, adaptive fuzzy control technique, being a model independent control paradigm for complex and uncertain systems, is a good choice for such systems. In this work, a hydraulic dead zone compensated robust adaptive fuzzy control law has been proposed for locomotion control of hydraulically actuated hexapod demining robot. The experimental results exhibit a fairly accurate trajectory tracking of the leg joints and, consequently, very stable locomotion of the walking robot.

This paper describes the implementation and validation of a fuzzy inference engine for estimating human affective state in real-time, using robot motions as the stimulus. The inference engine was tested with 36 subjects. To the authors' knowledge, this paper reports the first such trial that measures affective response to human-scale physical robot motions for a statistically significant population. The results demonstrate that affective state arousal can be detected using physiological signals and the inference engine. Comparison of results between the two planners shows that subjects report less anxiety and surprise with the safe planner.

Dynamic simulation of a flexible manipulator performing physical contact (including low-speed impact) tasks with stiff environment is very time consuming because very small integration step sizes have to be used for numerical stability. Existing model order reduction techniques cannot be readily applied due to the nonlinear nature of the contact dynamics. In this paper, a method is introduced to deal with this problem. The method first linearizes the contact force model on the right-hand side of the dynamics equations periodically. It then identifies the linear “stiffness” and “damping” terms from the linearized contact force model and combines them with the existing structural stiffness and damping matrices of the associated multibody system on the left-hand side of the equations. After such a process, the traditional modal analysis and reduction techniques for linear dynamic systems can be applied to reduce the order of the resulting dynamic system. Two numerical examples of flexible manipulators performing a contact task are presented to demonstrate the significant gain in computational efficiency and the improved output results.

The significance of singularities in the design and control of robot manipulators is well known, and there is an extensive literature on the determination and analysis of singularities for a wide variety of serial and parallel manipulators—indeed such an analysis is an essential part of manipulator design. Singularity theory provides methodologies for a deeper analysis with the aim of classifying singularities, providing local models and local and global invariants. This paper surveys applications of singularity-theoretic methods in robot kinematics and presents some new results.

Algebraic methods in connection with classical multidimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. In this paper, we give an overview of the results achieved within the last few years using the algebraic geometric method, geometric preprocessing, and numerical analysis. We provide the mathematical and geometrical background, like Study's parametrization of the Euclidean motion group, the ideals belonging to mechanism constraints, and methods to solve polynomial equations. The methods are explained with different examples from mechanism analysis and synthesis.

An autonomous mobile robot operating in an unknown indoor environment often needs to map the environment while localizing within the map. Feature-based world models including line and point features are widely used by researchers. This paper presents a novel delayed-classi-fication algorithm to categorize these features using a recently developed high-performance sonar ring within a simultaneous localization and map-building (SLAM) process. The sonar ring sensor accurately measures range and bearing to multiple targets at near real-time repetition rates of 11.5 Hz to 6 m range, and uses 24 simultaneously fired transmitters, 48 receivers and multiple echoes per receiver. The proposed algorithm is based on hypothesis generation and verification using the advanced sonar ring data and an extended Kalman filter (EKF) approach. It is capable of initiating new geometric features and classifying them within a short distance of travel of about 10 cm. For each new sonar reading not matching an existing feature, we initiate a pair of probational line and point features resulting from accurate range and bearing measurements. Later measurements are used to confirm or remove the probational features using EKF validation gates. The odometry error model of the filter allows for variations in effective wheel separation required by pneumatic robot tyres. The implementation of the novel classification and SLAM algorithm is discussed in this paper and experimental results using real sonar data are presented.

While a robot moves, online hand–eye calibration to determine the relative pose between the robot gripper/end-effector and the sensors mounted on it is very important in a vision-guided robot system. During online hand–eye calibration, it is impossible to perform motion planning to avoid degenerate motions and small rotations, which may lead to unreliable calibration results. This paper proposes an adaptive motion selection algorithm for online hand–eye calibration, featured by dynamic threshold determination for motion selection and getting reliable hand–eye calibration results. Simulation and real experiments demonstrate the effectiveness of our method.

Many applications require unmanned ground vehicles (UGVs) to travel at high speeds on sloped, natural terrain. In this paper, a potential field-based method is proposed for UGV navigation in such scenarios. In the proposed approach, a potential field is generated in the two-dimensional “trajectory space” of the UGV path curvature and longitudinal velocity. In contrast to traditional potential field methods, dynamic constraints and the effect of changing terrain conditions can be easily expressed in the proposed framework. A maneuver is chosen within a set of performance bounds, based on the local potential field gradient. It is shown that the proposed method is subject to local maxima problems, rather than local minima. A simple randomization technique is proposed to address this problem. Simulation and experimental results show that the proposed method can successfully navigate a small UGV between predefined waypoints at speeds up to 7.0 m/s, while avoiding static hazards. Further, vehicle curvature and velocity are controlled during vehicle motion to avoid rollover and excessive side slip. The method is computationally efficient, and thus suitable for onboard real-time implementation.

In this paper, we focus on the development of a quantitative performance analysis framework for a cooperative system of multiple wheeled mobile manipulators physically transporting a common payload. Each mobile manipulator module consists of a differentially driven wheeled mobile robot (WMR) with a mounted planar three-degree-of-freedom (DOF) revolute-jointed manipulator. A composite cooperative system is formed when a payload is placed at the end-effectors of many such modules. The system possesses the ability to change its relative configuration as well as to accommodate relative positioning errors of the wheeled agents. However, the combination of nonholonomic constraints due to the mobile bases, holonomic constraints due to the closed kinematic loops, and the different joint-actuation schema (active/passive/locked) within the system requires careful quantitative evaluation to efficiently realize the payload manipulation task. Hence, in this paper, we extend the differential kinematic model for treatment of constrained articulated mechanical systems to formulate a framework to include both the mixture effect of holonomic/nonholonomic constraints and the different possible joint-actuation schema in our system. The system-level performance is then examined quantitatively by the manipulability measure in terms of isotropy index with representative case studies.

Wheeled Mobile Manipulators (WMM) possess many advantages over fixed-base counterparts in terms of improved workspace, mobility and robustness. However, the combination of the nonholonomic constraints with the inherent redundancy limits effective exploitation of end-effector payload manipulation capabilities. The dynamic-level redundancy-resolution scheme presented in this paper decomposes the system dynamics into decoupled task-space (end-effector motions/forces) and a dynamically consistent null-space (internal motions/forces) component. This simplifies the subsequent development of a prioritized task-space control (of end-effector interactions) and a decoupled but secondary null-space control (of internal motions) in a hierarchical WMM controller. Various aspects of the ensuing novel capabilities are illustrated using a series of simulation results.

In this paper, the authors use the conformal geometric algebra in robotics. This paper computes the inverse kinematics of a robot arm and the differential kinematics of a pan–tilt unit using a language of spheres showing how we can simplify the complexity of the computations.

This work introduces a new geometric Jacobian in terms of bivectors, which is by far more effective in its representation as the standard Jacobian because its derivation is done in terms of the projections of the involved points onto the line axes. Furthermore, unlike the standard formulation, our Jacobian can be used for any kind of robot joints.

In this framework, we deal with various tasks of three-dimensional (3D) object manipulation, which is assisted by stereo-vision. All these computations are carried out using real images captured by a robot binocular head, and the manipulation is done by a five degree of freedom (DOF) robot arm mounted on a mobile robot. In addition to this, we show a very interesting application of the geometric Jacobian for differential control of the binocular head. We strongly believe that the framework of conformal geometric algebra can generally be of great advantage for visually guided robotics.

Free-flying space manipulator systems, in which robotic manipulators are mounted on a free-flying spacecraft, are envisioned for assembling, maintenance, repair, and contingency operations in space. Nevertheless, even for fixed-base systems, control of mechanical manipulators is a challenging task. This is due to strong nonlinearities in the equations of motion, and consequently different algorithms have been suggested to control end-effector motion or force, since the early research in robotic systems. In this paper, first a brief review of basic concepts of various algorithms in controlling robotic manipulators is introduced. Then, specific problems related to application of such systems in space and a microgravity environment is highlighted. Basic issues of kinematics and dynamics modeling of such systems, trajectory planning and control strategies, cooperation of multiple arm space free-flying robots, and finally, experimental studies and technological aspects of such systems with their specific limitations are discussed.