Hierarchical least-square optimization is often used in robotics to inverse a direct function when multiple incompatible objectives are involved. Typical examples are inverse kinematics or dynamics. ...The objectives can be given as equalities to be satisfied (e.g. point-to-point task) or as areas of satisfaction (e.g. the joint range). This paper proposes a complete solution to solve multiple least-square quadratic problems of both equality and inequality constraints ordered into a strict hierarchy. Our method is able to solve a hierarchy of only equalities 10 times faster than the iterative-projection hierarchical solvers and can consider inequalities at any level while running at the typical control frequency on whole-body size problems. This generic solver is used to resolve the redundancy of humanoid robots while generating complex movements in constrained environments.
Forward and backward reaching inverse kinematics (FABRIK) is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix. ...Based on FABRIK, this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect. Due to the characteristics of FABRIK, it can induce large angular movements on specific joints. Apart from that, FABRIK maps three dimensional (3D) problem into two dimensional (2D) problem by a simple geometric projection. This operation can cause infinite loops in some cases. In order to overcome these issues and apply FABRIK on space manipulators, an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector. The manipulator is re-positioned based on the momentum conservation law. Instead of pure target position tracking, the orientation control of the end-effector is also considered. Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.
The human musculoskeletal system is characterized by redundancy in the sense that the number of muscles exceeds the number of degrees of freedom of the musculoskeletal system. In practice, this means ...that a given motor task can be performed by activating the muscles in infinitely many different ways. This redundancy is important for the functionality of the system under changing external or internal conditions, including different diseased states. A central problem in biomechanics is how, and based on which principles, the complex of central nervous system and musculoskeletal system selects the normal activation patterns, and how the patterns change under various abnormal conditions including neurodegenerative diseases and aging. This work lays the mathematical foundation for a formalism to address the question, based on Bayesian probabilistic modeling of the musculoskeletal system. Lagrangian dynamics is used to translate observations of the movement of a subject performing a task into a time series of equilibria which constitute the likelihood model. Different prior models corresponding to biologically motivated assumptions about the muscle dynamics and control are introduced. The posterior distributions of muscle activations are derived and explored by using Markov chain Monte Carlo (MCMC) sampling techniques. The different priors can be analyzed by comparing the model predictions with actual observations.
•We develop Bayesian methodology to study muscle recruitment problem.•Feasible solutions are explored using Markov chain Monte Carlo.•Longitudinal priors control smoothness of the activation trajectories.•Potential applications include surgery planning and rehabilitation.
Soft manipulators are safer as human-robot interaction devices thanks to their inherent characteristics, such as flexibility, lightweight structure, and security. However, it is difficult to ...precisely control multi-segment, high-dimensional soft manipulators due to their uncertain model deformation and external disturbance. This paper develops a dual-segment variable cross-section pneumatic soft manipulator (PSM) fabricated by integrated manufacturing to solve this problem. Easier to establish inverse kinematics model (IKM), neural network IKM is trained using the PSM motion datasets. However, the neural network fitted IKM still suffers from significant position errors. In this paper, an improved control strategy combining neural network IKM and iterative feedback tuning (IFT) controller based on sensors is proposed to reduce the positioning error of the PSM tip. Two kinds of IFT laws are presented, compared, and analyzed to verify the feasibility and optimality of the control strategy through numerical simulation. By point-to-point tracking and load experiments, the method was proved to achieve 1 mm (0.27 %), which demonstrated that the improved positioning control strategy could effectively improve the accuracy of PSM under both no-load and load conditions. Finally, the dual-segment variable cross-section PSM application performance is accomplished in actual manipulation tasks.
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•A variable cross-section pneumatic soft manipulator is designed and fabricated using variable hardness material.•A novel closed-loop control scheme combined with an IFT controller is presented to compensate for positioning error.•Experiments demonstrate that the method effectively solves the high-precision positioning control of the soft manipulator.•This control strategy combines simplicity and accuracy and can be extended to multi-segment continuum robot applications.
This paper presents a novel analytic method to uniquely solve inverse kinematics of 7 degrees-of-freedom manipulators while avoiding joint limits and singularities. Two auxiliary parameters are ...introduced to deal with the self-motion manifolds: the global configuration (GC), which specifies the branch of inverse kinematics solutions; and the arm angle (ψ) that parametrizes the elbow redundancy within the specified branch. The relations between the joint angles and the arm angle are derived, in order to map the joint limits and singularities to arm angle values. Then, intervals of feasible arm angles for the specified target pose and global configuration are determined, taking joint limits and singularities into account. A simple metric is proposed to compute the elbow position according to the feasible intervals. When the arm angle is determined, the joint angles can be uniquely calculated from the position-based inverse kinematics algorithm. The presented method does not exhibit the disadvantages inherent to the use of the Jacobian matrix and can be implemented in real-time control systems. This novel algorithm is the first position-based inverse kinematics algorithm to solve both global and local manifolds, using a redundancy resolution strategy to avoid singularities and joint limits.
Since parallel mechanisms (PMs) have good stiffness, accuracy, and dynamic characteristics, a large number of PMs have been invented recently. A few kinds of them are found to have excellent ...performances, and one kind is two-rotational and one-translational (2R1T) PM. The existing research on 2R1T PMs shows that this kind of mechanism has outstanding rotational properties and a well-translational workspace. Many 2R1T mechanisms with good performances have been proposed, among which the typical ones are 3PRS, 2UPR-SPR, and 3UPS-UP. Based upon the existing 2R1T mechanisms, a new 2R1T mechanism, 2UPR-PRS, is proposed and analyzed in this paper, which combines PRS and UPR chains, respectively, from 3PRS and 2UPR-SPR together. In this way, the high stiffness provided by the PRS chain and the variable rotational characteristics from two symmetric UPR chains are integrated into the proposed 2UPR-PRS mechanism. First, the conceptual design of this mechanism is carried out. Second, its inverse kinematics is solved. Finally, the mobility of the mechanism is analyzed by a newly developed method through a parameterizing twist in a continuous motion manner, and its kinematic model is thus formulated, revealing the rotational characteristics of the mechanism with the variable axis.
Inverse kinematics (IK) is the use of kinematic equations to determine the joint parameters of a manipulator so that the end effector moves to a desired position; IK can be applied in many areas, ...including robotics, engineering, computer graphics and video games. In this survey, we present a comprehensive review of the IK problem and the solutions developed over the years from the computer graphics point of view. The paper starts with the definition of forward and IK, their mathematical formulations and explains how to distinguish the unsolvable cases, indicating when a solution is available. The IK literature in this report is divided into four main categories: the analytical, the numerical, the data‐driven and the hybrid methods. A timeline illustrating key methods is presented, explaining how the IK approaches have progressed over the years. The most popular IK methods are discussed with regard to their performance, computational cost and the smoothness of their resulting postures, while we suggest which IK family of solvers is best suited for particular problems. Finally, we indicate the limitations of the current IK methodologies and propose future research directions.
Inverse kinematics (IK) is the use of kinematic equations to determine the joint parameters of a manipulator so that the end effector moves to a desired position; IK can be applied in many areas, including robotics, engineering, computer graphics and video games. In this survey, we present a comprehensive review of the IK problem and the solutions developed over the years from the computer graphics point of view. The paper starts with the definition of forward and IK, their mathematical formulations and explains how to distinguish the unsolvable cases, indicating when a solution is available.
Abstract The installation of the high-altitude curtain wall is mainly completed manually with simple mechanical assistance. The construction process is characterized by high labor intensity, high ...risk, low efficiency and low quality. To improve the automation and intelligence of curtain wall installation, improve construction efficiency and reduce labor intensity, a mobile manipulator for curtain wall installation is developed. Firstly, the curtain wall installation process is analyzed. Secondly, kinematics modeling is established, and the forward and inverse kinematics are analyzed and solved. Finally, the experiment is carried out to complete the tasks of grasping, rolling over and transporting stone, glass, ALC plate and other dense and semi-dense materials.
Elastomer-based soft-continuum robots with an extensible backbone exhibit high flexibility. These manipulators might show nonlinear kinematic behaviors due to, for example, the material ...hyperelasticity and means of actuation. Formulating a reliable kinematic model for an effective inverse kinematics control strategy is challenging, but is paramount for allowing effective manoeuvrability and controllability. In this article, we devise a kinematic modeling and control method for pneumatic-driven soft-continuum robots (up to 100% elongation ratio). The method is based on the Cosserat rod model including a pressure-dependent dynamic modulus. The kinematic model and control strategy are then expressed as nonlinear least-squares optimization problems. Hence, various inverse kinematics control modes can be achieved for a multisegment robot, e.g., tip position and orientation control of the overall robot or tip position control of each segment. Simulations and experiments are both conducted to validate the proposed method. The results highlight the high fidelity of the modeling technique and the effectiveness of the proposed inverse kinematics controller. In particular, the modeling and trajectory control errors for a two-segment robot are smaller than 4.5 mm, i.e., 5% of the robot's overall length.
The absolute differential cross section for small-angle proton elastic scattering on the proton-rich 8B nucleus has been measured in inverse kinematics for the first time. The experiment was ...performed using a secondary radioactive beam with an energy of 0.7 GeV/u at GSI, Darmstadt. The active target, namely hydrogen-filled time projection ionization chamber IKAR, was used to measure the energy, angle and vertex point of the recoil protons. The scattering angle of the projectiles was simultaneously determined by the tracking detectors. The measured differential cross section is analyzed on the basis of the Glauber multiple scattering theory using phenomenological nuclear-density distributions with two free parameters. The radial density distribution deduced for 8B exhibits a halo structure with the root-mean-square (rms) matter radius Rm=2.58(6) fm and the rms halo radius Rh=4.24(25) fm. The results on 8B are compared to those on the mirror nucleus 8Li investigated earlier by the same method. A comparison is also made with previous experimental results and theoretical predictions for both nuclei.
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