A novel method for the contouring control of robot manipulators

In this paper, a new asinh-type control scheme with gravity compensation for the position control problem of robot manipulators in joint space is presented. The properties and characteristics of the asinh control structure make the position error and the motion velocity asymptotically converge to the equilibrium point. A strict Lyapunov function to formally prove global asymptotic stability is developed. The tuning of the control gains is obtained by PSO (Particle Swarm Optimization) technique without saturating the servomotors. To illustrate the effectiveness and performance of the proposed scheme, an experimental comparative analysis between the proportional-derivative (PD) and atanh controls against the proposed algorithm on a three degrees of freedom direct-drive robot manipulator is carried out.

A principle of ‘joint‐space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real‐time from a Jacobian matrix of the constraint equation in joint coordinates.To show the important role of the principle in control of robot manipulators, two basic set‐point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi‐natural potential and the joint‐space orthogonalization. Various stability problems of PID‐type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper‐stability theory.

We consider the tracking control problem for robot manipulators whose parameters are not exactly known. It is assumed that some unmodelled friction is acting at the actuated joints. The proposed solution guarantees that the disturbances on the outputs (the joint positions) can be attenuated by an arbitrary factork. For the setpoint regulation problem a self‐tuning controller is proposed. In this case the disturbances (uncertain parameters and unmodelled non‐linearities) on the outputs are completely rejected asymptotically. Some simulation results are included.

This article presents a visual-inertial-based control strategy to address the task-space control problem for robot manipulators. To achieve this, a hybrid observer is introduced for visual-inertial odometry, enabling the control loop to be closed directly in Cartesian space by estimating the end-effector pose. The end-effector is equipped with an inertial measurement unit (IMU) and a stereo camera, which provide task-space feedback information to the proposed observer. A hybrid controller is then designed to utilize the estimated end-effector pose for accurate motion control. The Lyapunov stability theorem is employed to demonstrate that the resulting closed-loop system, using the proposed observer-based controller, is globally and asymptotically stable. Besides this notable merit (global asymptotic stability), the proposed method also reduces the impact of robot kinematics on the controller’s performance. Real-world experiments and computer simulations using a six-degrees-of-freedom (DoFs) long-reach hydraulic robot manipulator are conducted to evaluate the performance of the proposed observer-based control scheme.

The path tracking control problem of robot manipulators carrying unknown payloads is studied on the basis of the payload-dependent robot model and its structural properties. The nonlinear payload-dependent dynamic model of a robot manipulator is derived, and several structure properties of this model are investigated. On the basis of these properties, a path tracking control strategy is presented. It is shown that the presented strategy not only compensates for the effects of couplings, nonlinearities, and payload uncertainty but also guarantees tracking convergence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A dynamic feedback controller will be proposed to treat the trajectory tracking control problem of robotic manipulators with flexible joints that use only position measurements on the link and motor sides. Previously published results for the tracking control problem without velocity measurements address only the rigid robot design. Moreover, these results are based on a full-order observer whose dimension is equal to the dimension of the robotic systems. In contrast, our solution can be applied to treat the robotic systems with flexible joints. It does not require any restriction on the joint stiffness. The proposed controller is based on a reduced-order observer which is constructed only to estimate the velocity signal and whose dimension is half of the dimension of flexible-joint robotic systems. We shall show that the resulting closed-loop error system is locally exponentially stable with an arbitrarily large region of attraction. The convergence rate can be arbitrarily pre-assigned and the attraction...

In this paper, we mainly solve the adaptive control problem of robot manipulators with uncertain kinematics, dynamics, and actuators parameters, which has been a long-standing, yet unsolved problem in the robotics field, because of the technical difficulties in handling highly coupled effect between control torque and the mentioned uncertainties. To overcome the difficulties, we propose a new Lyapunov-based adaptive control methodology, which effectively fuses the inverse Jacobian technique and the actuator adaptation law, with which the chattering in tracking errors caused by actuator parameter perturbation is well suppressed. It is demonstrated that the asymptotic convergence of all closed-loop signals is guaranteed. Moreover, the effectiveness of our control scheme is illustrated through simulation studies.

This paper addresses the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control problem for robot manipulators using unit dual quaternion representation, which allows an utter description of the end-effector transformation without decoupling rotational and translational dynamics. We propose three different H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control criteria that ensure asymptotic convergence, whereas reducing the influence of disturbances upon the system stability. Also, with a new metric of dual quaternion error in SE(3) we prove independence from robot coordinate changes. Simulation results highlight the importance and effectiveness of the proposed approach in terms of performance, robustness, and energy efficiency.

This paper deals with the control problem of robotic manipulators, which are always subject to nonlinear uncertainties. In particular, a dynamic system with fast actuators is exposed to many disrupting risks, generally induced by the presence of parametric uncertainties and unmoderated dynamics. So the dynamic model becomes highly nonlinear, which requires the use of a robust stabilising control. In this context, we propose a solution based on the third order sliding mode control (SMC) approach, in order to ensure a performant trajectory tracking motion control for a medical task. The proposed controller is expected to remove the standard sliding mode restrictions, to provide for a higher accuracy and robustness in realisation with respect to the current existence of imperfections. Simulation results confirm the effectiveness of the proposed third order SMC design with respect to disturbances, mainly affecting control systems.

The time-optimal path following (OPF) problem is to find a time evolution along a prescribed path in task space with shortest time duration. Numerical solution algorithms rely on an algorithm-specific (usually equidistant) sampling of the path parameter. This does not account for the dynamics in joint space, that is, the actual motion of the robot, however. Moreover, a well-known problem is that large joint velocities are obtained when approaching singularities, even for slow task space motions. This can be avoided by a sampling in joint space, where the path parameter is replaced by the arc length. Such discretization in task space leads to an adaptive refinement according to the nonlinear forward kinematics and guarantees bounded joint velocities. The adaptive refinement is also beneficial for the numerical solution of the problem. It is shown that this yields trajectories with improved continuity compared to an equidistant sampling. The OPF is reformulated as a second-order cone programming and solved numerically. The approach is demonstrated for a 6-DOF industrial robot following various paths in task space.

Chapter 1 - Terminology and general definitions

As Human-Robot Interaction (HRI) develops, robots are expected to learn more complex and demanding interaction skills. Complex HRI tasks are often embodied in robots that are jointly constrained by task space and joint space. In the field of Imitation Learning, scholars have explored the topic of joint constraints from task space and joint space, but there are few relevant studies in Human-Robot Interaction. In this paper, based on the Interaction Primitives framework (a HRI framework), we propose an interaction inference method that first generalizes the robot's movements in two spaces synchronously and then probabilistically fuses the two movements based on Bayesian estimation. This work was validated in the task that the robot follows a human handheld object, and the inference errors (RMSE and MAE) of the method are smaller in both task space and joint space than in IP using only singlespace inference.

Before moving a robot arm, it is of considerable interest to know whether there are any obstacles present in its path. Computer-based robots are usually served in the joint space, whereas objects to be manipulated are usually expressed in the Cartesian space because it is easier to visualize the correct end-effector position in Cartesian coordinates than in joint coordinates. In order to control the position of the end-effector of the robot, an inverse kinematics (IK) solution routine should be called upon to make the necessary conversion (Fu et al., 1987). Solving the inverse kinematics problem for serial robot manipulators is a difficult task; the complexity in the solution arises from the nonlinear equations (trigonometric equations) occurring during transformation between joint and Cartesian spaces. The common approach for solving the IK problem is to obtain an analytical close-form solution to the inverse transformation, unfortunately, close-form solution can only be found for robots of simple kinematics structure. For robots whose kinematics structures are not solvable in close-form; several numerical techniques have been proposed; however, there still remains several problems in those techniques such as incorrect initial estimation, convergence to the correct solution can not be guarantied, multiple solutions may exist and no solution could be found if the Jacobian matrix was in singular configuration (Kuroe et al., 1994; Bingual et al., 2005). A velocity singular configuration is a configuration in which a robot manipulator has lost at least one motion degree of freedom DOF. In such configuration, the inverse Jacobian will not exist, and the joint velocities of the manipulator will become unacceptably large that often exceed the physical limits of the joint actuators. Therefore, to analyze the singular conditions of a manipulator and develop effective algorithm to resolve the inverse kinematics problem in the singular configurations is of great importance (Hu et al., 2002). Many research efforts have been devoted towards solving this problem, one of the first algorithms employed was the Resolved Motion Rate-Control method (Whitney, 1969), which uses the pseudoinverse of the Jacobian matrix to obtain the joint velocities corresponding to a given end-effector velocity, an important drawback of this method was

In this paper, we propose two simple adaptive iterative learning control (AILC) algorithms for trajectory tracking control problem of rigid robot manipulators that track the same control trajectory repeatedly over a finite time interval. The design comprises of a linear parameterization robot feedback control structure and a learning parametric adaptation law that iteratively updates unknown uncertain parameters based upon the use of a Lyapunov energy function. In contrast to other existing adaptive ILC schemes for robot manipulators, where large feedback and learning gains are required to get robustness against large modelling uncertainties and disturbances in the early stage of the operation, the proposed adaptive ILC schemes require small feedback gains. The presented scheme 2 is simpler in structure and easier to implement in the real-world operation in the sense that it requires less computational effort and computing power without any priori knowledge of robot dynamics. Owing to the robustness of the adaptation laws against large disturbances and modelling uncertainties in the early trials, a high-learning gain can be used in order to achieve fast learning convergence.

Position-based visual servo control of autonomous robotic manipulators