Workspace Boundary Research Articles

Analysis of Reachable Workspace for Spatial Three-Cable Under-Constrained Suspended Cable-Driven Parallel Robots

Abstract The workspace is an important reference for designs of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literature study the workspaces of under-constrained CDPRs. In this paper, the static equilibrium reachable workspaces (SERWs) of spatial 3-cable under-constrained CDPRs are solved numerically since expressions describing workspace boundaries cannot be obtained in closed forms. The steps to solve the SERWs are as follows. First, expressions that describe the SERWs and their boundaries are proposed. Next, these expressions are instantiated through a novel anchor points model composed of linear equations, quadratic equations, and tension limits in cables. Then, based on the reformulated linearization technique (RLT), the constraints system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of the branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by two examples. One is searching the SERWs boundaries of a special three-cable-driven parallel robot (CDPR) whose anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by a method to extract the SERW boundary where cables do not interfere with each other. The other is searching the SERWs boundaries of a general three-cable CDPR with randomly selected geometry arrangement. The presented method in this paper is universal for calculating the SERWs of spatial three-cable CDPRs with arbitrary geometry parameters.

Design and experimental validation of a disturbing force application unit for simulating spacecraft separation

The separation of the heatshield and backshell as the spacecraft enters the atmosphere and decelerates is a highly challenging task during the exploration of an exoplanet. Owing to its high complexity, few experimental validations have been performed so far for this separation process. In this paper, a novel disturbing force application unit is designed, which can simulate the disturbing forces and disturbing moments. It is deployed in a cable-driven parallel mechanism which is used to simulate the heatshield and backshell separation. This cable-driven parallel mechanism is presented from the aspects of mechanical design, kinematic analysis, dynamic analysis, numerical simulation, and experimental validation. First, the kinematic and dynamic model of the cable-driven parallel mechanism is established. Then, the definition of disturbing force controllable workspace is proposed. The workspace quality coefficient, which checks whether the end-effector is close to the workspace boundary, is presented. The configuration design is discussed. Third, numerical simulations are implemented to investigate the effects of axial forces, disturbing forces and disturbing moments on the end-effector position and orientation. Finally, an experimental platform is built. Experimental verification of the separation of the heatshield and backshell in different conditions are implemented. A series of experimental results show that both heatshield and backshell are safely separated from the lander. The proposed cable-driven parallel mechanism can accurately simulate the disturbing force during the separation process of the heatshield and the backshell.

An Optimal Motion Cueing Algorithm Using the Inverse Kinematic Solution of the Hexapod Simulation Platform

The vehicle motion signals is not able to be replicated using the simulation-based motion platform (SBMP) because of the workspace boundaries. The workspace limitations are determined based on the displacement, velocity and acceleration limitations of the actuators. The motion cueing algorithms (MCAs) are introduced to reproduce the motion sensation for the driver of the SBMP same as the real vehicle's driver while keeping the SBMP inside the actuators' limitations. The optimal MCA was developed to decrease the human motion sensation error between the real vehicle's driver and the SBMP's user based on the human vestibular system model using the linear quadratic regulator method. However, the inverse acceleration kinematics model of the SBMPs are not considered in developing optimal MCA to control the displacement, velocity and acceleration of actuators. The lack of inverse acceleration kinematics consideration inside the optimal MCA causes the poor consumption of the SBMP's workspace, as the optimal MCA only considers the boundaries of the SBMP in the Cartesian coordinate system. In this paper, the new optimal MCA based on the inverse acceleration kinematic solution of the SBMP is designed and developed to regenerate the more realistic motion sensation. The validation of the new optimal MCA is performed using Simulink/MATLAB. The outcomes demonstrate that using the new optimal MCA will reach a better motion sensation with less false motion signals in contrast with the existing optimal MCAs.

Devising a method to analyze the current state of the manipulator workspace

This paper has proposed a program analysis method over the current state of the workspace of an anthropomorphic manipulator using the Mathcad software application package (USA). The analysis of the manipulator workspace helped solve the following sub-tasks: to calculate the limits of the grip reach, to determine the presence of "dead zones" within the manipulator workspace, to build the boundaries of the manipulator workspace. A kinematic scheme of the manipulator typically provides for at least five degrees of mobility, which is why in the three-dimensional Cartesian coordinate system the work zone boundaries represent the surfaces of a complex geometric shape. The author-devised method makes it possible to construct the projections of the boundaries of the manipulator's work zone onto the coordinate planes in the frame of reference associated with the base of the robot.
 Using Mathcad's built-in features makes it possible to effectively solve the above sub-tasks without wasting time developing specialized software. The Mathcad software application package provides for the possibility of a symbolic solution to the first problem of the kinematics of an industrial robot, that is, the program generates analytical dependences of the coordinates for special point P (pole) of the grip on the trigonometrical functions of the generalized coordinates. The resulting analytical dependences are used for kinematic and dynamic analysis of the manipulator.
 Special features in constructing mathematical models when using the Mathcad software application package have been revealed. Simulating the manipulator movement taking into consideration constraints for kinematic pairs, the drives' power, as well as friction factors, makes it possible to optimize the parameters of the manipulator kinematic scheme.
 An example of the analysis of the working space of an anthropomorphic manipulator with five degrees of mobility has been considered.
 The reported results could be used during the design, implementation, modernization, and operation of manipulators.

Numerical simulation of the workspace of robots with moving bases in the multi-agent system

Multi-robotic systems are used to solve many practical tasks in wide areas, including military surveillance, reconnaissance, rescue operations, warehousing, etc. Such systems can be represented as groups of intelligent robots capable of interacting with each other and jointly implementing various tasks. One of the problems in the development of such systems is the safe navigation of a group of robots. The restrictions imposed by the structural elements of its agents are determined to solve it. The article presents the structure of a multi-robotic system consisting of parallel and serial robots installed on mobile platforms. The parallel robot is made based on a tripod with the possibility of rotating the robot base about the horizontal axis. Determining the workspace boundaries of robots eliminates collisions between agents and external objects. The developed algorithms are based on deterministic methods for approximating the solutions set of nonlinear inequalities systems with restrictions in spaces of coordinates in the form of n-dimensional boxes. The relative positions of mobile platforms with manipulators, at which collisions are possible, are determined.

Singularity analysis and avoidance of a planar parallel mechanism with kinematic redundancy under a fixed orientation

In this paper, the singularity of a planar mechanism with kinematic redundancy is studied. First, the architecture of the mechanism and the concept schematic diagram for singularity avoidance are stated. Next, inverse kinematics model of the planar parallel mechanism with kinematic redundancy is established. For determining the unique inverse solution of the mechanism under certain initial installation configuration, a comparison analysis based on the strategy tree and the virtual prototype is performed. Then, based on the obtained Jacobian matrices and the singular condition, the workspace-singularity map and two singular configurations of the mechanism are drawn. Finally, with the obtained workspace-singularity map, a singularity-free transition layer and an aisle can be found to perform to singularity avoidance, even if the initial designed trajectory passing through the second kind of singularity. Three tasks are carried out to illustrate that the workspace boundary and singular configuration can be changed by adjusting the kinematic redundant actuated parameter.

Fuzzy-Based Fault-Tolerant Control for Omnidirectional Mobile Robot

The motion-planning problem is well known in robotics; it aims to find a free-obstacle path from a starting point to a destination. To make use of actuation generosity and the fuzzy fast response behavior compared to other non-linear controllers, a fuzzy-based fault-tolerant control for an omnidirectional mobile robot with four Mecanum wheels is proposed. The objective is to provide the robot with an online scheme to control the robot motion while moving toward the final destination with avoiding obstacles in its environment and providing an adaptive solution for a combination of one or combination of the wheel’s faults. The faults happen when the wheel does not receive the control command signal from the controller; in this case, the robot can rotate freely due to the interaction with the ground. The principle of fuzzy-based control proposed by Sugeno is used to develop the motion controller. The motion controller consists of two main controllers: the Run-To-Goal, and the obstacle-avoidance controller. The outputs of these two controllers are superposed to get the net potential force on the robot. By its simplicity, the fuzzy controller can be suitable for online applications (online path planning in our case). To the best of our knowledge, this is the first fuzzy-based fault-tolerant controller for an omnidirectional robot. The proposed controller is tested by a set of simulation scenarios to check the proposed fuzzy tolerant control. Kuka OmniRob is used as an example of the omnidirectional robot in these simulation runs. Matlab is used to build the fuzzy-based fault-tolerant control, and the 3D simulation is developed on the CoppeliaSim software. We examine five distinct scenarios, each one with a different fault state. In all scenarios, the proposed algorithm could control the robot to reach its final destination with the absence and presence of an obstacle in the workspace, despite actuator faults, without crossing the workspace boundaries.

Identification of the parallel 3-PRRR manipulator parameters considering the workspace boundaries and the passive orthosis movements

The article discusses a system of rehabilitation of the lower extremities based on a passive orthosis in the form of a sequential RRRR mechanism and an active parallel 3-PRRR robot. Effective numerical methods and algorithms were developed and tested that made it possible to determine the minimum geometric parameters of the active parallel mechanism that ensure the movement of a passive orthosis within the working area in accordance with clinical data when simulating walking. The simulation results are presented by visualizing the exported workspaces in the STL format.

The study of the accuracy of the robot movement along a given path considering the workspace boundaries, velocity and inertial properties of the drive

The paper considers the accuracy characteristics of a robot machine with a parallel structure as a control object. A specifically developed model of a planar 3-RPR mechanism with an electric drive based on a DC motor made it possible to experimentally study the dependence of the following robot output link accuracy according to the speed, weight and size characteristics of the drive and mechanism.

A Motion Cueing Algorithm Based on Model Predictive Control Using Terminal Conditions in Urban Driving Scenario

The motion cueing algorithm (MCA) is in charge of the real vehicle motion feeling regeneration for the driver of the simulation-based motion platform (SBMP) with respect to its limitations. The model predictive control (MPC) has been newly employed in developing MCAs to calculate the optimal input signals for delivering the best motion feeling to the SBMP's drivers while respecting the boundaries of the platform. The stability of the MCA based on MPC has become one of the main issues for some scenarios, such as an urban driving scenario, which involves sudden decelerations/accelerations (stop and start moving), sharp and large turn, and slalom movement. The urban driving scenario destabilizes the current MCA based on MPC and leads the undesired motion fluctuations, which create an unpleasant motion artifact for the SBMP drivers. Therefore, the displacement of the SBMP should be penalized conservatively to respect the workspace boundaries for all driving scenarios. This will make the motion conservative and can cause some motion-feeling error. In this article, the concept of terminal conditions (weights and states) are employed for the first time to design and develop a new generation of MCA based on MPC to enhance the performance of the model for different scenarios, such as the heavy-traffic scenario in the urban areas. Also, the stability of the MPC by considering the terminal conditions is investigated in the MCA domain. Then, the MCA based on MPC by considering terminal conditions is developed using the MATLAB software with a presentation of the urban motion scenario. The outcomes demonstrate the effectiveness of the designed model with a common MCA based on MPC without the consideration of the terminal conditions.

A sliding mode-based approach to motion cueing for virtual reality gaming using motion simulators

Motion simulators have been of significant importance for the aviation sector in training pilots. However, the present boom in the utilization of robotics for virtual reality (VR) gaming has given rise to a new application of motion simulators. Motion cueing algorithms (MCA) play a key role in mapping the motions from a gaming scenario to the workspace of a simulator. This workspace is small (as compared to the gaming world), and on reaching the boundary, it becomes necessary to saturate the motion. Each degree of freedom, in the Cartesian space, is saturated between two fixed extremities. This hampers the perception of motion of a user enjoying the scenario. In order to address this practical problem, we make an attempt to enlarge the workspace and develop a mathematical methodology to prevent the simulator from exiting a non-cuboidal workspace. To do so, we propose sliding mode-based cueing algorithm (SMCA), which makes the simulator to slide in close proximity across the boundary of workspace. We make use of discrete-time models to present this methodology in order to ensure straightforward implementation by researchers in the future. Veracity of SMCA is testified by means of experimentation on SP7 motion simulator. The experimental results give evidence of a 57% increase in the considered sub-workspace, thereby reducing the relative necessity to saturate the motions as compared to classical MCA. This leads to a better experience of a user enjoying the VR scenario. On the other hand, the following drawbacks are reported: (1) necessity to analytically model the workspace boundary and ensuring that it is smooth with nonzero gradient, (2) SMCA parameter selection is more cumbersome than classical MCA, thereby making its utility restricted to recorded scenarios.

Methodological approach for workspace boundary determination in joint space using support vector machine

For most industrial robots using position control, self-collision is a headache. Without well-defined constraints at a joint level, self-collision can lead to damage to a robot or even injury to the operator. In this study, a new methodological approach is proposed that is different from the traditional methods of using sensors or analysing kinematics. The proposed method uses a support vector machine to construct a joint boundary map based on the robot's movement in the workspace. To verify its feasibility and performance, simulations are conducted. The proposed method is believed to help reduce the cost and computational burden. It is expected to be utilised even in applications where the existing methods are difficult to use.

Stereovision Tracking System for Monitoring Loader Crane Tip Position

This paper presents the idea and experimental tests of a non-stationary stereovision system used for supervision of a loading crane. The system based on two independent gimbals, equipped with cameras, allows simultaneously to measure and track a group of individual spatial points. The four steps calibration procedure is required for each gimbal axis, camera optics, gimbals positions, and loading crane position. Modern camera systems have been widely applied in several fields of the industry allowing for accurate measurements and real-time quality control. The systems based on stereo camera models and appropriate image analysis algorithms can measure a group of spatial points, complex surfaces, small displacements, or vibrations. There are also several vision systems such as laser tracker, camera mounted on fully controlled rotating head (called gimbal), or TOF camera, which can be used to follow and measure real-time object displacements. Unfortunately, they all have significant individual limitations explained in this paper. Accuracy tests of 3D measurements including active tracking of length pattern and crane tip have been performed within a selected working area. Based on reconstructed 3D data points, different types of geometric errors have been presented. The results revealed effects of accuracy degradation on the workspace boundaries and for higher observation angles, as well as 3D data bias suggesting mechanical issues. Several improvements in calibration and gimbal construction might result in far enough accuracy for normal operations of the crane.

Design of a 4 DOF parallel robot arm and the firmware implementation on embedded system to transplant pot seedlings

This paper presents a firmware design and its implementation on a real time embedded system for driving a 4 DOF parallel robot arm. The firmware primarily comprised of two components to produce motion of the robot arm: a) generation of continuous position coordinates and b) generation of actuating signals. These two components were processed in two different microcontrollers with a common communication bus. The position generation algorithm produced and transmitted continuous position data to the motion generation algorithm in the form of G-code strings by reading the input positions which were previously stored by the user in EEPROM memory of the microcontroller. The receipt of a handshake signal synchronized the data transmission between these components through a communication bus. An LCD display and keypad were used as human-machine interface (HMI) to communicate with the user to set the robot target coordinates. The mechanical structure of the robot arm comprised of multiple links which were actuated by stepper motors. The workspace boundary were sensed by limit switches. The kinematic equations represented the gripper position for the corresponding input joint angles. A microcontroller was used to compute kinematic equations of the robot arm with the help of motion generation algorithm to generate actuation signals for the simultaneous movement of robot joints. The kinematic equations were solved with the dual-core capability of the microcontroller using real time operating system (RTOS), which made the computation faster with an average computation time of 198 μs per step. The developed firmware was implemented and tested on a 4 DOF parallel manipulator using embedded microcontrollers for continuous pickup and place of the paper pot seedlings for automating the metering of pot seedlings. The cycle time taken for pickup and dropping of each seedling was 3.5 s with a success rate of 93.3%.

Kinematics and dynamics analysis of the 3PUS-PRU parallel mechanism module designed for a novel 6-DOF gantry hybrid machine tool

A hybrid kinematic machine (HKM) tool with the respective advantages of serial and parallel mechanism is a significant direction for the innovation and development of current advanced sophisticated manufacturing equipment. This paper considers the configuration design, kinematics analysis and dynamics analysis of a 1-translational-3-rotational (1T3R) parallel manipulator, which acts as the main movement module of a novel 6-DOF reconfigurable HKM. The key parallel manipulator with 4 DOFs is composed of one middle PRU kinematic chain and three identical PUS kinematic chains. First, complete kinematics characteristics, including position, velocity, acceleration and jerk, are deeply analyzed by a vector analysis approach. Reachable position workspace and orientation workspace were derived through the workspace boundary search method. Furthermore, complete inverse dynamics model of the 3PUS-PRU parallel manipulator was formulated by virtue of the virtual work principle with considering the inertial and gravitational properties of struts. Finally, a driving power and energy consumption model of each actuated motor under the prescribed trajectory were obtained, resulting in the decouple contribution of each motion part correspondingly. This systematic and rigorous methodology aims at laying a solid theoretical and technical foundation for configuration design and performance analysis of this homologous type HKM.

Maximizing the failure-tolerant workspace area for planar redundant robots

Kinematically redundant robots have extra degrees of freedom so that they can tolerate a joint failure and still complete an assigned task. Previous work has defined the “failure-tolerant workspace” as the workspace that is guaranteed to be reachable both before and after an arbitrary locked-joint failure. One mechanism for maximizing this workspace is to employ optimal artificial joint limits prior to a failure. This current work presents a technique for determining these optimal artificial joint limits that is based on the gradient ascent method. The proposed technique is able to deal with the discontinuities of the gradient that are due to changes in the boundaries of the failure tolerant workspace. The technique is illustrated using two examples of three degree-of-freedom planar serial robots. The first example is an equal link length robot where the optimal artificial joint limits are computed exactly. In the second example, both the link lengths and artificial joint limits are determined, resulting in a robot design that has more than twice the failure-tolerant area of previously published locally optimal designs.

A Robust Predictive Control Approach for Underwater Robotic Vehicles

This article presents a robust nonlinear model predictive control (NMPC) scheme for autonomous navigation of underwater robotic vehicles operating in a constrained workspace including the static obstacles. In particular, the purpose of the controller is to guide the vehicle toward specific way points with guaranteed input and state constraints. Various constraints, such as obstacles, workspace boundaries, predefined upper bounds for the velocity of the robotic vehicle, and thruster saturations, are considered during the control design. Moreover, the proposed control scheme is designed at dynamic level, and it incorporates the full dynamics of the vehicle in which the ocean currents are also involved. Hence, taking the thrusts as the control inputs of the robotic system and formulating them accordingly, the vehicle exploits the ocean current dynamics when these are in favor of the way-point tracking mission, resulting in reduced energy consumption by the thrusters. The robustness of the closed-loop system against parameter uncertainties has been analytically guaranteed with convergence properties. The performance of the proposed control strategy is experimentally verified using a 4 degrees of freedom (DoF) underwater robotic vehicle inside a constrained test tank with sparse static obstacles.

Workspace analysis and trajectory tracking of a planar hybrid manipulator with ball screw feed drive

The hybrid manipulators have benefits of both serial as well as parallel manipulators. In this paper, a planar hybrid manipulator with six degrees-of-freedom is proposed; it consists of two parallel manipulators each having three degrees-of-freedom. The models for forward and inverse dynamic analysis of this manipulator are presented with bond graph approach. The actuators of the manipulator have ball screw feed drive mechanism to convert rotary motion into linear motion. There are basically three problems addressed in the paper. First, the models are simulated for trajectory tracking of a semi-circular path traced by the lower manipulator initially and then tracking of another semi circular path by upper manipulators. The second problem addressed is to develop the bond graph model of the hybrid manipulator with proportional control to reach a desired position from an initial position with an unity slope after few seconds. Finally, workspace analysis for given semi-circular trajectory is done with calculation of area of the workspace of lower, upper and hybrid manipulators. It is observed from the simulation that the response follows the desired trajectory within the permissible limit. The result indicates that manipulator follows nearly tangential path. It is seen from the result that the desired trajectory lies within the workspace boundary.

Fault-tolerant strategy and workspace of the subreflector parallel adjusting mechanism

Parallel mechanism has been widely used in large-scale and heavy-duty attitude adjustment equipment. In order to improve the work reliability of the subreflector parallel adjusting mechanism, a fault-tolerant strategy based on the redundant degree-of-freedom and a workspace boundary identification method are proposed in this paper, which can realize the proper function of the subreflector parallel adjusting mechanism when it has a driven fault. The configuration and parameters of the parallel adjusting mechanism are introduced firstly, then the degrees-of-freedom of the parallel adjusting mechanism is calculated when it has a driven fault, and the principle of the fault-tolerant strategy based on the redundant degree-of-freedom is deduced in detail. Next, the method to solve the workspace boundary identification problem for the parallel adjusting mechanism in fault tolerance conditions is proposed, the maximum and minimum workspaces of the parallel adjusting mechanism at fault tolerance conditions in different frequency bands are analyzed. The results showed that the workspace calculated by the fault-tolerant strategy in the fault condition can completely meet the needs of the subreflector, where this method can also be applied to other parallel mechanisms. Lastly, an experiment is conducted to verify the correctness and effectiveness of the fault-tolerant strategy, in which the results showed that the fault-tolerant strategy can effectively improve the work reliability of the parallel adjusting mechanism. The fault-tolerant strategy and workspace boundary identification method can make the subreflector parallel adjusting mechanism work normally when it has a driven fault, which can significantly improve the work reliability and work efficiency and the maintenance cost can also be reduced. The fault-tolerant strategy and workspace boundary identification method can also be well applied to the research and development for this kind of parallel mechanical equipment.

Image-Guided Mastoidectomy with a Cooperatively Controlled ENT Microsurgery Robot.

Mastoidectomy is a common surgical procedure within otology. Despite being inherently well suited for implementation of robotic assistance, there are no commercially available robotic systems that have demonstrated utility in aiding with this procedure. This article describes a robotic technique for image-guided mastoidectomy with an experimental cooperatively controlled robotic system developed for use within otolaryngology-head and neck surgery. It has the ability to facilitate enhanced operative precision with dampening of tremor in simulated surgical tasks. Its kinematic design is such that the location of the attached surgical instrument is known with a high degree of fidelity at all times. This facilitates image registration and subsequent definition of virtual fixtures, which demarcate surgical workspace boundaries and prevent motion into undesired areas. In this preliminary feasibility study, we demonstrate the clinical utility of this system to facilitate performance of a cortical mastoidectomy by a novice surgeon in 5 identical temporal bone models with a mean time of 221 ± 35 seconds.