Rolling contact kinematics plays a vital role in dexterous manipulation and rolling-based locomotion. Yet, in practical applications, the environments and objects involved are often captured as discrete point clouds, creating substantial difficulties for traditional motion control and planning frameworks that rely on continuous surface representations. In this work, we propose a differential geometry-based framework that models point cloud data for continuous rolling contact using locally parameterized representations. Our approach leverages skeletonization to define a rotational reference structure for rolling interactions and applies a Fourier-based curve fitting technique to extract and represent meaningful controllable local geometric structure. We further introduce a novel 2D manifold coordinate system tailored to arbitrary surface curves, enabling local parameterization of complex shapes. The governing kinematic equations for rolling contact are then derived, and we demonstrate the effectiveness of our method through simulations on various object examples.

A simulator is a software application that allows imitating an experimental environment and controlling a process or an instrument. Projects in human-robot interaction (HRI) field face different challenges during real world experiments, which include improper robot behavior, mistakes in an algorithm logic, software and hardware failures, and generic lay participants on a user side. Simulators could help to avoid a number of problems that researchers would definitely face within real world experiments at algorithms' testing stage. This study presents an experimental validation in Gazebo simulator and real-world experiments for English language lessons scenarios with a small size humanoid Robotis DARwin OP2. We investigated advantages of using Gazebo simulator in constructing modular generic HRI blocks and global HRI scenarios in order to optimize a humanoid robot assisted process of studying English. The simulator saved a significant amount of efforts and time at preparatory stages, allowing robot programmers and HRI developers to obtain a quick feedback from users and their requirements for necessary adjustments.

Robot simulators provide an easy way for evaluation of new concepts and algorithms in a simulated physical environment reducing development time and cost. Therefore it is convenient to have a tool that quickly creates a 3D landscape from an arbitrary 2D image or 2D laser range finder data. This paper presents a new tool that automatically constructs such landscapes for Gazebo simulator. The tool converts a grayscale image into a 3D Collada format model, which could be directly imported into Gazebo. We run three different simultaneous localization and mapping (SLAM) algorithms within three varying complexity environments that were constructed with our tool. A real-time factor (RTF) was used as an efficiency benchmark. Successfully completed SLAM missions with acceptable RTF levels demonstrated the efficiency of the tool. The source code is available for free academic use.

Motion control of underactuated systems through the inverse dynamics contains configuration singularities. These limitations in configuration space mainly stem from the inertial coupling that passive joints/bodies create. In this study, we present a model that is free from singularity while the trajectory of the rotating mass has a small-amplitude sine wave around its circle. First, we derive the modified non-linear dynamics for a rolling system. Also, the singularity regions for this underactuated system is demonstrated. Then, the wave parameters are designed under certain conditions to remove the coupling singularities. We obtain these conditions from the positive definiteness of the inertia matrix in the inverse dynamics. Finally, the simulation results are confirmed by using a prescribed Beta function on the specified states of the rolling carrier. Because our algebraic method is integrated into the non-linear dynamics, the proposed solution has a great potential to be extended to the Lagrangian mechanics with multiple degrees-of-freedom.

This position paper deals with formalization of a practical scenario of using multiple aerial robots for monitoring an expanding area, which is a part of an operational framework and a global information system for real-time management of flood disasters caused by torrential rains. Two typical tasks of the optimal information coverage problem, represented by caging the disaster area and tracking its dynamic expansion are sketched. Three basic component of the minimal configuration of the control system-the image segmentation, Kalman filtering based tracking, and distributed formation control-are identified and reviewed.

This paper deals with motion planning and control problems for a class of partially differentially flat systems. A Betafunction based motion planning algorithm is first constructed by selecting the base variable to be the 2-nd order derivative of Beta-function weighted by a constant parameter. The proposed algorithm has lower computational cost than the optimal control while it provides similar system performance. Then, a function approximation technique based control algorithm is proposed by restructuring a partially differentially flat system in the form of the combination of an auxiliary linear system and its variation from the original system. The variation term was replaced by its approximation as a chosen basis function weighted by constant parameters to be determined. These unknown plant parameters are estimated at each instant, denoted by the adjustable control parameters using a defined update law.

This paper describes process of development of communication protocol for group of mobile robots in Urban Search and Rescue (USAR) operations based on wireless technology and Robot Operating System framework. During this work cases of mobile robot's usage in USAR as well as modern worldwide researches in this area were studied and it was found out that one of the main issues with mobile robot usage in such situation is communication problem. Disasters typically destroy communication infrastructure and rescuers forced to use workarounds to be able to still use robots. Based on these studies goal for the paper has been set - to develop communication protocol that allows robots to communicate and exchange data with minimal human interference. To achieve this goal multiple types of communication technologies were analyzed and Bluetooth was chosen based on qualities most suited for this task. After that list of commands needed for USAR was combined and three of them (Follow, Stop, MoveAround) were chosen to be implemented during this research. Testing environment was created in simulator Gazebo with three TurtleBot robots to verify execution of developed command. Finally, commands and command handler were implemented and tested on robots in created testing environment by using trial scenarios.

Recent developments in 3D reconstruction systems enable to capture an environment in great detail. Several studies have provided algorithms that deal with a path-planning problem of total coverage of observable space in time-efficient manner. However, not much work was done in the area of globally optimal solutions in dense clutter environments. This paper presents a novel solution for autonomous exploration of a cluttered 2.5D environment using an unmanned ground mobile vehicle, where robot locomotion is limited to a 2D plane, while obstacles have a 3D shape. Our exploration algorithm increases coverage of 3D environment mapping comparatively to other currently available algorithms. The algorithm was implemented and tested in randomly generated dense clutter environments in MATLAB.

Most of robots are using vision for various applications. In some cases, mobile robots are provided with an insufficient onboard processing hardware, and therefore video from cameras needs to be transmitted in an efficient and reliable way to a more powerful system for further off-board processing. Multiple difficulties could be faced during video streaming software development, including high latencies, network congestion, packet losses, distortions and others, which makes trade-offs between video quality, bitrate, frame rate, and packet loss inevitable. Thus, the key problem is to find such parameters, which will satisfy the specified needs. In our work we implement a video streaming server on mobile robot Servosila Engineer. A set of experiments demonstrated that high bitrates and frame rates increase load on CPU. Packet losses could be mitigated by decreasing bitrate to 100-200 kbps.

The paper deals with modeling of human-like reaching movements in dynamic environments. A simple but not trivial example of reaching in a dynamic environment is the rest-to-rest manipulation of a multi-mass flexible object with the elimination of residual vibrations. In this movement task, the hand velocity profiles may have a form that is quite different from the classical bell shape. Two approaches to the prediction of reaching movements are formulated in position and force actuation settings. In the first approach, either the position of the hand or the hand force is specified by the lowest order polynomial satisfying the boundary conditions of the reaching task. The second approach is based on the minimization of either the hand jerk or the hand force-change, with taking into account the dynamics of the flexible object. To verify the resulting four mathematical models, an experiment on the manipulation of a ten-masses flexible object of low stiffness is conducted. The experimental results show that the second approach gives a significantly better prediction of human movements, with the minimum hand force-change model having an edge over the minimum hand jerk one.

An adaptive trajectory tracking problem for a spherical rolling robot driven by a 2DOF pendulum is considered in this paper. A feedback controller is proposed for the goal of tracking the trajectory for the full configuration of the spherical robot. To deal with time-varying uncertainty of the system dynamics, an adaptation mechanism is included in the trajectory tracking controller by parameterizing the system uncertainty with a polynomial function, weighted by unknown constant parameters adjustable by the defined update law. The constructed controller is first tested for the planar hoop-pendulum and then applied to the ball-pendulum system. The convergence to the desired trajectories under the control law is proved and then verified by simulations for tracking circular motions under perturbation.

This paper deals with motion planning and control for an underactuated system, the hoop-pendulum, a pendulum mounted at the center of a hoop. The dynamic model for this system is derived and the local controllability around the equilibrium point is established. To transfer the system from a initial configuration to a desired final configuration in rest-to-rest mode, two controllers, the feedback and feedforward ones, are constructed. The feedback controller stabilizes the system at the origin and is based on the construction of a suitable Lyapunov function. The feedforward controller is based on the representation of the motion of the pendulum by the second derivative of Beta function. The feasibility and the performance of the proposed controllers are verified under simulations.

This paper deals with a trajectory tracking problem for the ball-pendulum system, a spherical rolling robot driven by a two degree of freedom pendulum. The backstepping technique is applied and first tested on the hoop-pendulum system, a planar case of the ball-pendulum. By mimicking the backstepping process of the planar case, a feedback controller for the ball-pendulum system is then proposed, tracking motion trajectories for both the position and orientation of the spherical shell of the rolling robot. The validity of the constructed tracking controller is demonstrated by establishing the asymptotic stability of the error dynamics for the closed-loop system. The performance of the controller is verified under simulations for tracking linear and circular motions.

The paper presents an analysis of human-like reaching movements in manipulation of parallel flexible objects. To predict the trajectory of human hand, a minimum hand jerk model, based on the minimization of integral of squared hand jerk over the movement duration is established. It is shown that within this model the optimal hand trajectory is composed of a fifth order polynomial and two trigonometric terms depending on the natural frequencies of the system and the movement time. A virtual reality-based experimental setup with a haptic simulator is designed, and the prediction by the minimum hand jerk model is verified against experimental data. The theoretical prediction matches the collected data with a reasonable accuracy. The initial experimental results confirm the applicability of the minimum hand jerk model for modeling of human-like reaching movements in dynamic environments.

Conventional motion planners for wheeled vehicles often assume no-slipping and no-skidding conditions and construct motion trajectories in the context of nonholonomic motion planning. However, in some practical situations slipping and skidding cannot be ignored or can even be useful. To take them into account in the construction of planning algorithms, it is important to model the friction force between the tire and the contact plane. In this paper, we first construct a model of the friction force as an extension of the two-dimensional Coulomb model, considering both the slipping conditions and the nonholonomic constraints. Next, we formulate the motion planning problem as a drift parking problem and propose a motion planning strategy combining the nonholonomic planner and the control in the slipping mode. The feasibility and the performance of the proposed strategy are tested under simulation.

This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First a dynamic model for the rolling robot is established. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a non-trivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, two possible approaches are suggested. A computational algorithm, implementing the motion planning strategy, is developed and verified under simulation.

This paper deals with motion planning problems for spherical rolling robots driven by a two degree of freedom pendulum. A full dynamic model for this system is first introduced. Then, assuming that the contact path is specified and the sphere moves in pure rolling mode, the full dynamic model is reduced by imposing virtual constraints. A timing control law, based on the Beta function, for tracing the contact curves in rest-to-rest motion is constructed. The constructed control law is verified under simulation for tracing Viviani's curve and the Loxodrome on the sphere.

Most motion planners for a vehicle often assume no-slipping and no-skidding in the context of nonholonomic motion planning. However, there actually exist slipping and skidding in practical situations and it is important to know the force between the tire and the contact plane considering slipping and skidding in the planning problem. In this paper, a Coulomb friction model of the tire friction force of vehicle is extended to nonholonomic constraints. In the modeling, the longitudinal and lateral tire friction forces are modeled corresponding to no slipping and no skidding constraints, respectively. A two directional model based on the maximum dissipation principle is also developed. Some typical movements of vehicles with the proposed friction force model are illustrated by simulations.

This paper deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The key feature of the problem is that it can be stated only in dynamic formulation. In addition, the problem features a singularity when the contact trajectory goes along the equatorial line in the plane of the two rotors. A motion planning strategy composed of two trivial and one nontrivial maneuver is devised. The trivial maneuvers implement motion along the geodesic line perpendicular to the singularity line. The construction of the nontrivial maneuver employs the nilpotent approximation of the originally nonnilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. The motion planning strategy thus constructed is verified under simulation.

The paper deals with the problem of motion planning for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. To solve the problem, we employ the so-called geometric phase approach based on the fact that tracing a closed path in the space of input variables results in a non-closed path in the space of output variables. To set up the governing equations, the contact kinematic equations are modified by the condition of dynamic realizability, which constrains the component of the angular velocity of the rolling carrier and depends on the mass distribution, and parameterized. By using a motion planning strategy based on tracing two circles on the spherical surface, an exact and dynamically realizable motion planning algorithm is fabricated and verified under simulation.

The paper deals with the dynamics and motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits non-holonomic constraints to propel the rolling carrier. The full mathematical model as well as its reduced version are derived, and the inverse dynamics is addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two orthogonal axes of the actuation the condition of dynamic realizability of a feasible kinematic trajectory is established. The implication of this condition to motion planning in dynamic formulation is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere surface the dynamically realizable trajectories are essentially different from those resulted from kinematic models.

The paper deals with the motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. It is shown that if the robot is actuated by three rotors, any feasible kinematic trajectory is dynamically realizable. For the case of two rotors the conditions of controllability and dynamic realizability of a feasible kinematic trajectory are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The dynamic motion planning problem is then formulated in the optimal control settings, and the properties of the optimal trajectories are illustrated under simulation.

A dynamic model of a flexible slewing beam in contact with the external environment is developed in this paper. The model is represented in the non-dimensional form. A definition of the percussion center of the flexible beam is introduced and its basic properties are established. It is shown that, contrary to the percussion center of rigid beam, for the flexible beam there exists infinite number of percussion centers, one for the first vibration mode, two for the second, three for the third and so on. It is also shown that the percussion centers can be considered as the points of maximal stiffness of the correspondent vibration modes. The results of our theoretical study may be interested not only for designing flexible tools but also for planning motion strategies for flexible manipulators interacting with the external environment.

The paper deals with modeling of human-like reaching movements using a probabilistic minimum variance model. A continuous formulation of the minimum variance model is developed and analyzed. The model features a parameter, having the meaning of the post-movement time period, whose assignment in a systematic way is not evident. To facilitate the situation and avoid the explicit specification of this parameter, the limiting case of the post-movement period tending to infinity is analyzed for several classes of the control plant. A connection between this limiting model and the conventional minimum control effort model is also established.

The paper deals with modeling of human-like reaching movements. Several models are under study. First, we consider a model of reaching movement that corresponds to the minimization of control effort. It is shown that this model is represented by the well-known Beta function. The representation can be used for the construction of fractional order models and also for modeling of asymmetric velocity profiles. The natural boundary conditions, defined in this part of the paper, can also be used in modeling asymmetric velocity profiles. Finally, we consider the minimum time formulation of the optimization problem and (for the n-th order integrator) find its analytical solution in the general form.

The paper deals with the motion planning for a rolling system with limited contact area. The system under consideration is represented by a hemispherical object that can roll without slipping or spinning on the plane. Under the constraints imposed on the size of the contact area, the construction of motion can be regarded as a problem of parallel parking in a finite number of movement steps. A motion planning algorithm, realizing the movement steps by tracing smooth figure eights on the hemisphere, is introduced. To generate asymmetric figure eights, a generalization of the Viviani curve is proposed. An exceptional case of the algorithm, corresponding to a spinning maneuver, is constructed with the use of the Cassini curve. The convergence of the algorithm is analyzed and its computational feasibility is verified under simulation.

The paper deals with modeling of human-like reaching movements using optimal control theory. Typically, in the construction of optimization models, capturing the invariant features of human movements, the main emphasis is placed on the form of the optimality criterion. However, the boundary conditions are also an important part of the optimization problem. Considering reaching movements in the manipulation of flexible objects, we first show that the conventional imposition of the boundary conditions does not always produce a good match to the experimental data featuring the acceleration jumps in highly dynamic tasks. To explain the acceleration jumps, we reformulate the problem, using the concept of natural boundary conditions, and show that it improves the prediction of the experimental data. Finally, it is suggested how not only the acceleration but all the boundary conditions can placed in a natural way.

The paper deals with the motion planning problem for a rolling sphere with limited contact area. The system under consideration is represented by a hemispherical object that can roll without slipping or spinning on the plane. Under the constraints imposed on the size of the contact area, the construction of motion can be regarded as a problem of parallel parking in a finite number of movement steps. A motion strategy, realizing the movement steps by tracing generalized figure eights on the hemisphere, is introduced. Two different algorithms for this motion strategy, the circle-based and the generalized Viviani-curve-based ones, are proposed. The convergence of the algorithms is analyzed, and the computational feasibility of these algorithms is verified under simulation.

The paper deals with motion planning for rolling-based systems with limited contact area. In a simplified formulation, the driving principle for such systems is based on controlling the position of the center of mass of the object, exploiting non-holonomic rolling constraint to propel the hemisphere. Two geometric algorithms for motion planning are formulated, analyzed, and tested under simulation. The simulation results show the possibility of moving the system to the desired configurations by steering the contact point on the hemisphere by generalized figure eights represented by circles and Viviani's curves.

The paper deals with the dynamics and motion planning for a rolling system with variable inertia. In a simplified formulation, the driving principle for the system under consideration is based on controlling the position of the center of mass of the object, exploiting non-holonomic rolling constraint to propel the hemisphere. We derive the dynamic model of this system and establish the condition of motion realizability. Providing that this condition holds true, we derive an approximate analytical solution for the trajectory of the particle, driving the system along a pre-specified path in the contact coordinates. The approximation is based on ignoring the quadratic velocity terms in the dynamic equations.

The paper deals with motion planning for rolling-based systems with limited contact area. To understand the problem we resort to a simplified quasi-static model in which the locomotion object is represented by a mass point. In this formulation, the driving principle is based on controlling the position of the center of mass of the object, exploiting nonholonomic rolling constraint to propel the hemisphere. Two motion planning algorithms are proposed. The algorithms are tested under simulation. The simulation results show the possibility of steering the locomotion system to the desired configurations by moving the center of mass through multiple generalized figure eights on the main hemisphere plane

The paper presents an analysis of human reaching movements in the manipulation of flexible objects. Two models, the minimum hand jerk and the minimum driving force-change, are derived and their basic features are analyzed. It is shown that the first model features two-phased hand velocity profiles, while in the second models there are multiple phases. The analysis of the phase transitions for the models considered is done in the analytical form. The results of this analysis can be helpful in the design of experimental scenarios for the verification of the theoretical models. Finally, we present some initial experimental results and analyze the applicability of the models developed in this paper

The paper presents an analysis of human reaching movements in manipulation of flexible objects. To predict the trajectory of human hand, a minimum crackle criterion has been recently introduced in literature. A different approach is explored in this paper. To explain the trajectory formation, we resort to the minimum hand jerk criterion. First, we show that this criterion matches well experimental data available in literature. Next, we argue that, contrary to the minimum crackle criterion, the minimum hand jerk criterion produces bounded hand velocity profiles for multimass flexible objects. Finally, we present initial experimental results confirming the applicability of the minimum hand jerk criterion to the prediction of reaching movements with multimass objects.

The paper presents an analysis of human reaching movements in manipulation of flexible objects. To predict the trajectory of human hand, a minimum crackle criterion has been recently proposed in literature. A different approach is explored in this paper. To explain the trajectory formation, we resort to the minimum hand jerk criterion. First, we show that this criterion matches well experimental data available in literature. Next, we argue that, contrary to the minimum crackle criterion, the minimum hand jerk criterion produces bounded hand velocity profiles for multi-mass flexible objects. Finally, we present initial experimental results confirming the applicability of the minimum hand jerk criterion in manipulation of multi-mass objects.

Constrained human movements are considered in this paper. The external constraints decrease the mobility of the human arm and lead to the redundancy in the distribution of the interaction force between the arm joints. To investigate the trajectory formation in the constrained human movements, we first develop a novel experimental system with interchangeable geometric constraints. Then, we examine the trajectory of human arm for an elliptic constraint. To clarify the trajectory formation in constrained point-to-point motions, we analyze experimental data and test them against predictions obtained by conventional criteria of optimality. It is found in the comparative analysis that the best prediction is given by the minimum muscle force change criterion.

A distributed PHANToM-based system for collaborative haptic visualization of a VR crank is presented. Physical IDOF crank model providing realistic kinaesthetic sensations of inertia and viscosity is described. Theoretical and experimental kinematic trajectory patterns are compared for the case of cooperative two-arm human movements. Nonvisual visualization applications of the system are discussed.

Opening a door, turning a steering wheel, rotating a coffee mill are typical examples of human movements constrained by the external environment. The constraints decrease the mobility of the human arm and leads to the redundancy in the distribution of the interaction force between the arm joints. Due to the redundancy of the force actuation in the constrained motions, there is infinite number of ways to form the trajectory of the arm. However, human forms the hand trajectory in a unique way. How does human resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate these problems, we examine the trajectory of human arm in a crank rotation task. To explain the trajectory formation in constrained point-to-point motions, we formulate an optimal control problem and propose a novel criterion minimizing the hand contact force change and muscle force change over the time of movement. The simulation results are compared with human motion and force profiles obtained experimentally. It is shown that the novel criterion captures the characteristics of the human constrained motion much more satisfactory than conventional criteria accepted in the research community.

The paper deals with the problem of the trajectory formation in human movements constrained by the external environment. To investigate this problem, we examine reaching movements of the human arm in a crank rotation task. The experimental data show that after learning and accommodation the position, velocity, and the tangential force trajectories converge to unique profiles while that of the normal force do not. To explain the formation of the human trajectories observed in the experiments, we resort to the optimization approach. Different criteria of optimality are analyzed using simplified kinematic and dynamic models. From the kinematic analysis we suggested that in the process of learning and adaptation the brain constructs a suitable parameterization of the constraint manifold. In the dynamic analysis it is found that the human trajectories cannot not be captured by a single conventional criterion. It is shown that a weighted combination of the hand force changes and the joint torque changes produces better results but brings the problem of weight selection.

Kinematics aspect of planning and control of human arm movements are considered in this paper. First, we analyze unconstrained reaching movements using simple analytical models. Here, we introduce a generalized minimum jerk criterion, analyze the smoothness of the optimal solutions and discuss the role of the boundary conditions in the trajectory formation. Next, we analyze the constrained human movements using a crank rotation task. Analysis of the experimental data shows that constrained and unconstrained reaching movements might involve different control strategies, which reflected in the choice of the optimality criterion. It is demonstrated that among the kinematics based criteria, the minimum crank jerk criterion produce a rough matching to the experimental data. It is hypothesized that in the process of learning and adaptation the brain constructs a suitable parameterization of the strained manifold.

Human hand can not only catch and grasp the complex objects but also easily manipulate the objects by switching various types of interactions. Research on the basic mechanics and control principles of hand's dexterous manipulation abilities is one of the most important subjects in bio-mimetics. In this paper, we formalize the multi-fingered hand manipulation problem as a general dynamic complementarity (DC) system. Based on the fact that the DC system can be transformed to a mixed logical dynamical (MLD) model, and that MLD system can control problem can be solved using powerful mixed integer programming (MIP) algorithm, we propose to realize dexterous hand manipulations by using a cyber-grasp system, and study its robotic realization on GIFU hand III, which is equipped with tactile sensors. We suggest that in order to obtain sub-optimal solutions, biologically inspired techniques might be very powerful.

An analysis of the stiffness of redundant manipulators is undertaken in this paper. First, the matrix of the force-dependent stiffness is derived and its basic properties are analyzed. In particular, in the planar case the stability conditions for the force dependent stiffness (and gravity-dependent stiffness) are obtained in the analytical form. Next, dual properties of the stiffness and compliance are exploited to establish a decomposition of the joint stiffness and compliance in the form similar to the decomposition of the joint velocities and torques. Finally, a minimal, nonredundant parameterization of the joint stiffness and compliance is commented.

This paper deals with a class of parallel mechanisms, called Gough-Stewart platforms. For these mechanisms, pre-loaded by driving forces, the stiffness matrix is derived and its basic properties are established. It is shown when the stiffness matrix becomes asymmetric, how the parametric imbalance may influence the system stability, and how the center of stiffness depends on the force pre-loading. Next, some necessary and some sufficient conditions for the stability are established in an analytical form by transforming the stiffness matrix to the center of stiffness.

Deals with a crank rotation task. The task requires coordinated movements of arm links without developing excessive internal forces. This research is directed, mainly, to the understanding of comfortable human movements constrained by the external environment. To get a deeper insight into the crank rotation task, we develop a mathematical model and analyze a weighted minimum norm muscle force distribution scheme that can be used in the resolution of the force redundancy. Analysis of experimental data shows that in comfortable motions a human is likely to modulate the rotational stiffness of the crank. This gives an additional constraint that can be used in the resolution of the force redundancy by optimization techniques.

This paper deals with the stability of a class of planar parallel mechanisms, called unifunctional manipulators. For this problem the stiffness matrix of the mechanisms is derived, and its basic properties are analyzed. Necessary and sufficient conditions for the stability are established in an analytical form by transforming the stiffness matrix to the center of stiffness. Next, at the level of force planning, the problem of stable force distribution is formulated. It is shown that an unstable force distribution can be stabilized by a simple control law if the mechanism is not in a singular configuration. Finally, conditions of the feedback stabilizability in singular configurations are established and illustrated on simple examples.

The paper deals with instance-based reinforcement learning control of autonomous robots. A classifier system, defined in the continuous state and action spaces, is outlined. Based on the sensory state space analysis, we define a learning strategy and fix the structure of the action rules. The classifier system features a nonconservative bucket brigade algorithm and a fast reproduction mechanism. The system developed is then applied to learning cooperative behavior by two robots coupled via a common object, with each robot controlled by its own classifier. The feasibility of this scheme is tested under experiment with two Lynxmotion robots, and a motion pattern of cooperative behavior (lifting up an object) is evolved using the two interacting classifier systems.

Deals with the rotational stability of a rigid body under constant contact forces. For this system, the stiffness tensor is derived, and its basic properties are analyzed. Necessary and sufficient conditions of positive definiteness of the stiffness tensor are established in an analytical form. Partial cases of the contact force distribution are analyzed. For the gravity-induced stiffness, conditions for stability are presented in terms of geometric and gravity centers. The internal forces are introduced with the use of a virtual spring model. Within this representation, conditions for stability under internal force loading are formulated in terms of the stiffness of the virtual springs.

Deals with the stability of a rigid body under multiple contact forces. First, the problem considered at the force planning level, and the stability of a force distribution is formulated. Analytical conditions for the stability of a force distribution, considered under unilateral frictional constraints, are studied on an illustrative example, Next, it is shown that stabilization of an unstable force distribution can be done by a simple control law. The stability conditions for this control law are formulated in terms of the force-induced stiffness tensor and the control-spring-induced stiffness tensor calculated at the stiffness center. Finally, comments on the contradiction between the Lyapunov stability and the contact stability of the objects are drawn.

The paper deals with the rotational stability of a rigid body under the constant internal forces. For this problem, first, the stiffness tensor is constructed and its basic properties are analyzed. The internal force parameterization is done with the use of the virtual linkage/spring model. Within this parameterization, necessary and sufficient conditions of stability are obtained in the analytical form. In the space of the internal forces they form a region given by intersection of a plane and a singular quadric. Since the stability conditions guarantee only positive definiteness of the stiffness tensor, the contact friction is taken into account separately. In this paper analysis of the unilateral constraints is done under a study case, where achieving stable grasp of a convex object, with the stretching internal forces created by friction, is studied in an analytical example.

A dynamic model of a flexible beam in contact with the environment is considered in this paper. The model serves as a background for a dynamic, active antenna type, contact point sensor. In its simplest realization the sensor can be implemented in the form of a flexible beam rotating in plane. The dynamic model is developed in the nondimensional form and possible sensing strategies, active and passive, are outlined. The main feature of the sensor is the use of the frequency-versus contact point curve which, for some regions, may be a multi-valued function. Basic properties of the sensing curves are formulated, and two points of interest-the point of maximal stiffness and the point of center of impact-are introduced into the analysis. Behaviour of the sensing curves is analyzed with respect to three system parameters-mass, inertia, and stiffness ratios. It is found that in some limiting, but practically attainable cases the sensing curve becomes a single-valued function within the working range of the sensor.

A dynamic active antenna sensor for locating a contact point is considered in this paper. In its simplest realization the sensor can be implemented in the form of a flexible beam rotating in plane. The main feature of the sensor is the use of the frequency-contact point curve which, for some regions, may be a multivalued function. One way of "improving" the curve could be concerned with the nonuniform mass and stiffness distribution of the beam which would lead to a rather complicated sensor design. Another way to remedy the situation is to change the sensing strategy by adding a proper control action at the joint of the beam. To study the sensor's response to the control, a dynamic model of the beam in contact with the external environment is developed. Analysis of the frequency equation shows how a simple proportional control law changes the sensing curve. It is found that in some limiting, but practically attainable cases the sensing curve becomes a single-valued function. Thus, the solution proposed can significantly simplify the identification procedure.

This paper discusses theoretical and experimental investigation, on dynamic active antenna which can detect the contact point between an insensitive flexible beam and an object through estimation of the oscillation frequency in contact with the object. We first prove that the contact position is uniquely determined if we consider every mode of natural frequencies of the beam in contact with the object, while the fundamental and the second order natural frequency, in most cases, satisfy the sufficient condition for providing the unique contact position. We also show a desirable mass distribution avoiding the estimation error for localizing the contact position. By utilising the maximum entropy method, we succeeded in experimental estimating the contact point from the fundamental and the second order natural frequencies.

In controlling manipulators interacting with the external environment, an important issue is the choice and construction of the Cartesian level control system. To effectively control the constrained manipulators, a knowledge of the resulting compliance of the system is required. In this paper a systematic analysis of the Cartesian stiffness and compliance matrices, which at full extent has not been undertaken in literature, is presented. A generalized model of a constrained flexible end-effector interacting with an elastic environment is developed on the basis of static and kinematic equations. The model developed is then applied to the case of several manipulators coupled through a common object.

An inverse kinematics problem of flexible manipulators is considered. The problem is of importance for compensation of tip deflections when the manipulators perform quasi-static operations. Based upon kinematic and static relationships, a definition of the inverse kinematic task of flexible manipulators is formulated. Specific features of the task are considered, and a conventional approach applicable for resolving the task is analyzed. To avoid disadvantages of the conventional approach, an implicit iterative scheme based upon step-by-step compensation for the relative elastic deflections is proposed. Corresponding convergence conditions of the scheme are derived, and applicability of the scheme is verified through simulation.>

This paper presents a systematic analysis of force sensors at the design stage. A generalized model of the sensors is developed on the basis of static and kinematic equations, and the block form of the resulting strain compliance matrix of the sensor is obtained. The model developed is then applied to the analysis of the two and three-dimensional sensor schemes corresponding to the regular polygons and polyhedrons. The condition number of the normalized strain compliance matrix of the sensor is used as the performance index. Impossibility of reaching the optimal values of this criterion is stated for the regular-polygon-form-based sensors. Partial solutions of the optimisation problem are found out for the regular-polyhedron-form-based sensors. The presentation of the material is illustrated by analytical examples.>

This paper presents a dynamic model and a control strategy for N robot arms cooperating through a flexible object. The dynamic equations of the system under consideration are derived, with position and force parameters being considered in an extended 6N-dimensional space. The control strategy is based on the decomposition of the position and force parameters. The strategy includes feedforward and feedback levels, which take into account the object compliance. The force and moments applied to the object by manipulators as well as the end-point accelerations are considered to be the control inputs for the Cartesian-level control system. The feedback level includes the nonlinear decoupling control law to ensure the tracking of the object trajectories in the position and force spaces. To damp out the object oscillations, an additional control input, which is added to the prespecified internal forces, is introduced. The applicability of the control strategy is tested under a case study.>

In the design of controlled manipulators, an important role is played by estimates of their mechanical properties, primarily the load capacity. The authors investigate, in a fixed configuration, the static load capacity of a system of manipulators transporting a common object. The problem of determining the load capacity is reduced to a general problem of linear programming whose solution can be obtained by using well-known numerical methods of optimization. On the basis of such a formalization of the problem, the lower and upper estimates of the load capacity are obtained. An analytic example is presented. Some comments on improving the methods of calculating the load capacity are made.>