Planar Manipulator Research Articles

Motion Planning by Sampling in Subspaces of Progressively Increasing Dimension

This paper introduces an enhancement to traditional sampling-based planners, resulting in efficiency increases for high-dimensional holonomic systems such as hyper-redundant manipulators, snake-like robots, and humanoids. Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a considerable challenge. The proposed enhancement to popular sampling-based planning algorithms is aimed at circumventing the exponential dependence on dimensionality, by progressively exploring lower dimensional volumes of the configuration space. Extensive experiments comparing the enhanced and traditional version of RRT, RRT-Connect, and Bidirectional T-RRT on both a planar hyper-redundant manipulator and the Baxter humanoid robot show significant acceleration, up to two orders of magnitude, on computing a solution. We also explore important implementation issues in the sampling process and discuss the limitations of this method.

Modeling, Calibration, and Evaluation of a Tendon-Actuated Planar Parallel Continuum Robot

In this work, a novel planar parallel continuum robot (PCR) is introduced, consisting of three kinematic chains that are coupled at a triangular end-effector platform and include tendon-actuated continuum segments. The kinematics of the resulting structure are derived by adapting the descriptions for conventional planar parallel manipulators to include constant curvature bending of the utilized continuous segments. To account for friction and non-linear material effects, a data-driven model is used to relate tendon displacements and curvature of the utilized continuum segments. A calibration of the derived kinematic model is conducted to specifically represent the constructed prototype. This includes the calibration of geometric parameters for each kinematic chain and for the end-effector platform. During evaluation, positioning repeatability of 1.0% in relation to one continuum segment length of the robot, and positioning accuracy of 1.4%, are achieved. These results are comparable to commonly used kineto-static modeling approaches for PCR. The presented model achieves high path accuracies regarding the robot's end-effector pose in an open-loop control scenario.

Exponentially convergence for the regressor-free adaptive fuzzy impedance control of robots by gradient descent algorithm

Having the capability to estimate parametric and non-parametric uncertainties, this paper investigates a regressor-free adaptive model-reference scheme for impedance control of robotic systems interacting with an environment. Using the gradient descent algorithm for designing a fuzzy estimator makes the tune of controller’s parameters possible in different physical situations and uncertainties. Thanks to the voltage control strategy and fuzzy systems, there is no need for designers to have the knowledge of robots and actuators’ dynamics. In addition, the force feedback is not employed in the structure of control law. Using the Lyapunov-like stability analysis, not only the exponential convergence of error signal and its time derivative to zero are guaranteed in the decentralised form but also the boundedness of all signals is ensured. To confirm the efficiency of proposed control algorithm, several simulations as well as a comparison with a positioned-based impedance controller and a regressor-based adaptive impedance controller are conducted on a two-link planar robot manipulator considering a tunable desired trajectory and different stiffness of environment. Additionally, the proposed adaptive impedance controller is applied to a six degree of freedom revolute-joint manipulator to provide better evaluation.

Self-Supervised Learning for Precise Pick-and-Place Without Object Model

Flexible pick-and-place is a fundamental yet challenging task within robotics, in particular due to the need of an object model for a simple target pose definition. In this work, the robot instead learns to pick-and-place objects using planar manipulation according to a single, demonstrated goal state. Our primary contribution lies within combining robot learning of primitives, commonly estimated by fully-convolutional neural networks, with one-shot imitation learning. Therefore, we define the place reward as a contrastive loss between real-world measurements and a task-specific noise distribution. Furthermore, we design our system to learn in a self-supervised manner, enabling real-world experiments with up to 25 000 pick-and-place actions. Then, our robot is able to place trained objects with an average placement error of (2.7 ± 0.2) mm and (2.6 ± 0.8) o . As our approach does not require an object model, the robot is able to generalize to unknown objects while keeping a precision of (5.9 ± 1.1) mm and (4.1 ± 1.2) o . We further show a range of emerging behaviors: The robot naturally learns to select the correct object in the presence of multiple object types, precisely inserts objects within a peg game, picks screws out of dense clutter, and infers multiple pick-and-place actions from a single goal state.

Réduction des erreurs de projection lors de la mesure de l’angle de Pauwels au cours des fractures du col fémoral par ajustement du plan tomodensitométrique

ObjectivesThe aim for the present study was to determine whether projection error of measuring Pauwels’ angle in young femur neck fracture could be eliminated by CT plane manipulation. MethodsClinical data of displaced femur neck fractures in young adults aged 20 to 64years old (13 females and 17 males) were retrospectively analyzed. Their average age was 47.9years (range, 22–64 years; SD, 11.3). Using modified measurement method for Pauwels’ angle using central line of the shaft as a guideline, the angle of a conventional coronal CT image was measured. CT images were imported into Mimics® software. The scanning plane was then reformatted parallel to the neck axis to eliminate projection error of injured limb. Measured angles were classified into three types (I<30°; II, 30–50°; and III>50°) and differences were analyzed. ResultsAverage Pauwels’ angle was 52.9° (range, 28.6–68.3°; SD, 9.9; type II, 17 cases; type III, 13 cases) for conventional CT images and 68.7° (range, 29.8–91.2°; SD, 13.4; type II, 1 cases; type III, 29 cases) for reformatted CT images. Difference between these two measurements on average was 15.7° (range, 1.2–34.9°; SD, 7.3) ConclusionsReformatting CT scanning plane by manipulating the proximal fragment to be parallel with the neck axis of the distal neck-shaft fragment is a convenient and reliable technique for eliminating the projection error of measuring Pauwels’ angle in the femur neck fractures. Level of evidenceIV, cohort study.

Time-dependent system kinematic reliability analysis for planar parallel manipulators

Time-dependent system kinematic reliability of the planar parallel manipulator refers to the probability of the pose error falling into the allowable safe region over the whole specified trajectory, which is essential for its work performance. However, works regarding this issue are quite limited. Consequently, this study conducts time-dependent kinematic reliability analysis for planar parallel manipulators considering joint clearance, input uncertainty, and manufacturing imperfection based on the first-passage method. First, the limit-state pose error function is established by means of the Baker–Campbell–Hausdorff formula and the theory of the Lie group and Lie algebra. Then, the analytical solution to the outcrossing rate of the non-stationary vector stochastic kinematic process is derived by employing the expectation propagation and closed-form properties of conditional and marginal statistical moments (mean and covariance) of the multivariate Gaussian. On this basis, the time-dependent system kinematic reliability is calculated upon the assumption that the outcrossing events are independent. Finally, the planar 3-RRR parallel manipulator is used to demonstrate the proposed method, and its effectiveness is validated by comparison with the Monte Carlo simulation method.

Quantitative objective-based ring TIRFM system calibration through back focal plane imaging.

Being the established imaging tool for cell membrane-associated studies, total internal reflection fluorescence microscopy (TIRFM) still has some limitations. The most important one is the inhomogeneous evanescent excitation field mainly caused by the large-angle and fixed-azimuth illumination scheme, which can be eliminated by using ring-shaped illumination (ring TIRFM). However, it is challenging in assembling a ring TIRFM system with precise parameter control that works well. Here we emphasize the quantification of the ring TIRFM system and introduce a robust calibration routine to simultaneously rectify the asymmetry of the spinning light beam and determine the crucial experimental parameter, i.e., the incident angle. The calibration routine requires no specific sample preparation and is entirely based on the automatic back focal plane manipulation, avoiding possible errors caused by the sample difference and manual measurement. Its effectiveness is experimentally demonstrated by both the qualitative and quantitative comparisons of the images acquired using different samples, illumination schemes, and calibration approaches. These characteristics should enable our approach to greatly improve the practicability of TIRFM in life sciences.

Optimum configuration design and sensitivity analysis of the 3-RRR PPMs with a general kinematic model

In this work, a parameterized model of 3-RRR planar parallel manipulator is proposed, aiming to optimize the overall performance with optimum shapes and sizes of the base and mobile platforms. In the model, the inverse and direct kinematics are addressed, upon which the global kinematic performance in terms of dexterity index is calculated and analyzed. A shape and dimensional optimization is accomplished through the atlas-based method. Optimum configurations are obtained from the global performance atlases. Moreover, sensitivity analysis of overall kinematic performance with respect to each configuration parameter of planar 3-RRR parallel manipulator is performed to reveal the influences of the design parameters. A case study is included to present a more detailed design of 3-RRR manipulator.

Virtual Model Reduction-based Control Strategy of Planar Three-link Underactuated Manipulator with Middle Passive Joint

This paper presents a position control strategy for a planar active-passive-active (APA) underactuated manipulator with second-order nonholonomic characteristics. According to the structural characteristics of the planar APA system, we divide the system into two parts: a planar virtual Pendubot (PVP) and a planar virtual Acrobot (PVA). For the PVP, we mainly fulfill the target angle of the first link, which is calculated through the geometry method, and make the system stable. In this stage, via keeping the states of the third link being zero, the system is reduced to the PVP. Meanwhile, we design an open-loop control law based on the nilpotent approximation (NA) model of the PVP to make the second link stable and the first link stabilize at its target angle. Then, the planar APA system is reduced to a PVA with all links’ angular velocities being zero. For the PVA, we mainly realize the other two links’ target angles obtained via the particle swarm optimization (PSO) algorithm. Thus, the control objective of the planar APA system is achieved. Finally, above control strategy is verified by simulation results.

Reactive planar non-prehensile manipulation with hybrid model predictive control

This article presents an offline solution and online approximation to the hybrid control problem of planar non-prehensile manipulation. Hybrid dynamics and underactuation are key characteristics of this task that complicate the design of feedback controllers. We show that a model predictive control approach used in tandem with integer programming offers a powerful solution to capture the dynamic constraints associated with the friction cone as well as the hybrid nature of contact. We introduce the Model Predictive Controller with Learned Mode Scheduling (MPC-LMS), which leverages integer programming and machine learning techniques to effectively deal with the combinatorial complexity associated with determining sequences of contact modes. We validate the controller design through a numerical simulation study and with experiments on a planar manipulation setup using an industrial ABB IRB 120 robotic arm. Results show that the proposed algorithm achieves closed-loop tracking of a nominal trajectory by reasoning in real-time across multiple contact modalities.

A general control strategy for planar 3-DoF underactuated manipulators with one passive joint

This paper presents a general control strategy based on the trajectory planning and tracking control for the planar 3-DoF underactuated manipulators with one passive joint at different position. According to the target position of the system, a set of target angles of all links are quickly obtained by using differential evolution algorithm. In order to achieve the control objective of the system from the initial position to the target position, we design the trajectory for each active link of the system, which is composed of two parts. The first part of the trajectory is designed according to the initial and target angle of the active link. The second part of the trajectory is designed based on the constraints between the passive joint and the active joints. Meanwhile, the parameters of the trajectories are optimized by the differential evolution algorithm to ensure that all links reach to their target angles eventually by tracking the designed trajectories. Then, the sliding mode variable structure controllers are designed to make all active links track their trajectories. The effectiveness of the proposed strategy is demonstrated through simulation results.

Dead Center Identification of Two-Degrees-of-Freedom Planar Parallel Manipulator Using Graph Theory and Transmission Angle

Abstract Parallel manipulators are widely applied for their advantages of high stiffness, load-bearing, operation speed, and precision positioning capabilities, which are required in many industrial applications. However, dead center identification is a challenging task and fundamental problem during design stage of parallel manipulators, and becomes more intractable for two-degrees-of-freedom (DOF) complex planar parallel manipulators (PPMs) design. This paper proposes a method to identify the dead center positions of two-DOF PPMs based on graph theory and transmission angle. First, these PPMs are denoted by a set of independent loops using a topological structural analysis of the kinematic chains and structural decomposition. Then, the relationship between the mobility factor and the loop factor in the same independent loop is utilized to obtain the folded or stretched operation to form the new PPMs containing the corresponding instantaneous virtual loop. Subsequently, the dead center positions can be located since the corresponding transmission angle of the new PPMs is equal to 0 deg or 180 deg. As a result, the solved dead center positions of the two-DOF three types seven-bar, nine-bar, and 11-bar PPMs will provide guidance for the proper design of these PPMs. Finally, the Jacobian method for identifying the dead center position is then used to verify the proposed method. The proposed method is systematic and programmable and can be applied to any two-DOF PPM regardless of the number of independent loops or types of joints.

Static Characteristic Analysis of Spatial (Non-Planar) Links in Planar Parallel Manipulator

SUMMARYConventional planar manipulators have their links in a single plane. Increasing payload at the end effector/mobile platform can induce high stress in the links due to the cantilever nature of links. Thus, it limits the total vertical load that can be applied on the mobile platform. In contrast to the links in conventional planar parallel mechanisms, non-planar links are proposed in this paper, that is, links are made inclined to the horizontal plane and non-planar legs are constructed. Though the links are made non-planar, the end effectors’ planar motion is retained. For studying the application of such non-planar links in planar manipulators, new models of inertia, stiffness and leg dynamics have to be developed. In this article, these models are developed by the static analysis of the planar manipulators with non-planar links, and the performance is compared with the corresponding conventional planar manipulators.

Trajectory Planning Using Artificial Potential Fields with Metaheuristics

The use of industrial robots has grown over the years, making production systems increasingly efficient. Within this context, some limitations appear that can delay the productive process causing damages to the production. These limitations are robot stops, for example. Stops can be caused by various factors, such as accidents, collisions of manipulator robots with operators or other equipment. The main contribution of this research is to improve the Artificial Potential Field (APF) using Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolution (DE) by optimizing the APF parameters in collision avoidance. We present as results: the trajectories generated by a planar manipulator robot; the position errors between the final position and the last position of the generated trajectories; and the computational cost of the PSO, GA and DE algorithms to find the parameters of the APF algorithm.

Disturbance Observer-Based Fault-Tolerant Control for Robotic Systems With Guaranteed Prescribed Performance

The actuator failure compensation control problem of robotic systems possessing dynamic uncertainties has been investigated in this paper. Control design against partial loss of effectiveness (PLOE) and total loss of effectiveness (TLOE) of the actuator are considered and described, respectively, and a disturbance observer (DO) using neural networks is constructed to attenuate the influence of the unknown disturbance. Regarding the prescribed error bounds as time-varying constraints, the control design method based on barrier Lyapunov function (BLF) is used to strictly guarantee both the steady-state performance and the transient performance. A simulation study on a two-link planar manipulator verifies the effectiveness of the proposed controllers in dealing with the prescribed performance, the system uncertainties, and the unknown actuator failure simultaneously. Implementation on a Baxter robot gives an experimental verification of our controller.

Position and posture control for a planar underactuated manipulator based on model reduction and chained structure

A control strategy is proposed based on the model reduction and the chained structure for a planar four-link (Active-Active-Passive-Active, AAPA) underactuated manipulator to achieve its position-posture control objective. The whole control process is divided into three stages. In the first stage, the planar AAPA manipulator is reduced to the planar virtual three-link (Active-Active-Passive, AAP) manipulator by controlling the angle of the fourth link and rotating it to zero. In the second stage, the model of a planar virtual AAP manipulator is transformed into the standard chain structure form. Then, the corresponding controllers are designed to control the passive joint of the planar virtual AAP manipulator to its target position, and the posture angle of the passive link is controlled to its middle posture angle at the same time. At the end of this stage, the planar AAPA manipulator is reduced to the planar Acrobot. In the third stage, the angle of the active link of the planar Acrobot is controlled to its target angle. Also, the angle control of the passive link of the system is realized. Consequently, the position-posture control objective of the planar AAPA manipulator is recognized. Considering the angle constraint of the planar Acrobot, the genetic algorithm is used to coordinate and optimize the target angle of the passive joint, the middle posture angle of the passive link, the target angle of the fourth link, and the target posture angle of the passive link. These ensure the target angles of the planar Acrobot corresponding to the target position-posture of the system can be found. Finally, simulation results demonstrate the effectiveness of the proposed control strategy.

A robust geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators

Jacobian-based methods of singularity analysis are known to be unreliable when applied to kinematically redundant parallel robot manipulators, due to their potential to miss certain singularities and incorrectly identify others in the manipulator’s workspace. In this paper, a geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators is presented, which firstly determines the manipulator’s proximity to a singularity and then computes how the kinematically redundant degree(s) of freedom should be optimised for the given pose of the end-effector. The singularity analysis is conducted by examining the mechanism in terms of the instantaneous centres of rotation of its corresponding mobility one sub-mechanisms when all but one of the actuators are locked, where the manipulator is in a type-II singularity when these points either are indeterminable or coincide with one another, and an index, rmin, is introduced which describes the minimum normalised distance from such conditions being met. A predictor-corrector method is employed to compute the configuration for which rmin is optimised, and is reachable without crossing a singularity. Finally, the advantages of the geometric method of singularity analysis are shown in comparison to traditional Jacobian-based methods when applied to kinematically redundant parallel robot manipulators.

Analysis of open-loop control design and parallel computation for underactuated manipulators

Trajectory tracking problems for underactuated manipulators represent an actual research topic, which is sustained by the interest in a lighter and faster automatic class of mechanical systems, bringing some benefits as lower energy consumption, higher productivity and a more convenient human–machine interaction. This work presents a feedforward design method, which is based on the inverse dynamics of underactuated manipulators. To achieve this aim, an optimal control problem is formulated based on a direct multiple shooting method and the mechanical model is formulated according to the nonlinear finite element approach. Based on the proposed formulation, a bounded solution of the inverse dynamics problem can be achieved. The main contributions of this work are: (1) the development of an alternative formulation for the trajectory tracking problem of underactuated manipulators; (2) a parallel computation method for the inverse dynamics of underactuated manipulators; (3) a comparison/validation with the direct transcription method and the stable inversion method. A planar underactuated manipulator with one passive joint is considered as an illustrative example, but the methodology is general and could be applied to more complex systems, e.g. with flexible bodies, with parallel kinematics and in 3D.

Time-Optimal Trajectory Planning for Flexible Joint Robots

In this letter, a new approach is proposed to optimally plan the motion along a parametrized path for flexible joint robots, i.e., robots whose structure is purposefully provided with compliant elements. State-of-the-art methods efficiently solve the problem in case of torque-controlled rigid robots via a translation of the optimal control problem into a convex optimization problem. Recently, we showed that, for jerk-controlled rigid robots, the problem could be recast into a non-convex optimization problem. The non-convexity is given by bilinear constraints that can be efficiently handled through McCormick relaxations and spatial Branch-and-Bound techniques. In this letter, we show that, even in case of robots with flexible joints, the time-optimal trajectory planning problem can be recast into a non-convex problem in which the non-convexity is still given by bilinear constraints. We performed experimental tests on a planar 2R elastic manipulator to validate the benefits of the proposed approach. The scalability of the method for robots with multiple degrees of freedom is also discussed.

One Robot for Many Tasks: Versatile Co-Design Through Stochastic Programming

Versatility is one of the main factors driving the adoption of robots on the assembly line and in other applications. Compared to fixed-automation solutions, a single industrial robot can perform a wide range of tasks (e.g., welding, lifting). In other platforms, such as legged robots, versatility is a necessity to negotiate varied terrains. The ability to balance performance across these anticipated scenarios is one of the main challenges to the process of design. To address this challenge, this letter proposes a new framework for the computational design of versatile robots by considering the interplay between mechanical design and control across multiple tasks and environments. The proposed method optimizes morphology parameters while simultaneously adjusting control parameters using trajectory optimization (TO) so that a single design can fulfill multiple tasks. As its main contribution, the letter details an approach to combine methods from stochastic programming (SP) with TO to address the scalability of these multi-task co-design problems. To assess the effects of this contribution, this letter considers the problems of designing a planar manipulator to transport a range of loads and a hopping monopod robot that must jump across a variety of terrains. The proposed formulation achieves faster solution times and improved scalability in comparison to state of the art co-design solutions. The resulting designs are also shown to be more versatile in terms of providing improved energy cost and task completion times across multiple scenarios.