TIP trajectory tracking of flexible-joint manipulators

In most robot applications, the control of the manipulator’s end-effector along a specified desired trajectory is the main concern. In these applications, the end-effector (tip) of the manipulator is required to follow a given trajectory. Several methods have been so far proposed for the motion control of robot manipulators. However, most of these control methods ignore either joint friction or joint elasticity which can be caused by the transmission systems (e.g. belts and gearboxes). This study aims at development of a comprehensive control strategy for the tip-trajectory tracking of flexible-joint robot manipulators. While the proposed control strategy takes into account the effect of the friction and the elasticity in the joints, it also provides a highly accurate motion for the manipulator’s end-effector. During this study several approaches have been developed, implemented and verified experimentally/numerically for the tip trajectory tracking of robot manipulators. To compensate for the elasticity of the joints two methods have been proposed; they are a composite controller whose design is based on the singular perturbation theory and integral manifold concept, and a swarm controller which is a novel biologically-inspired controller and its concept is inspired by the movement of real biological systems such as flocks of birds and schools of fishes. To compensate for the friction in the joints two new approaches have been also introduced. They are a composite compensation strategy which consists of the non-linear dynamic LuGre model and a Proportional-Derivative (PD) compensator, and a novel friction compensation method whose design is based on the Work-Energy principle. Each of these proposed controllers has some advantages and drawbacks, and hence, depending on the application of the robot manipulator, they can be employed. For instance, the Work-Energy method has a simpler form than the LuGre-PD compensator and can be easily implemented in industrial applications, yet it provides less accuracy in friction compensation. In addition to design and develop new controllers for flexible-joint manipulators, another contribution of this work lays in the experimental verification of the proposed control strategies. For this purpose, experimental setups of a two-rigid-link flexible-joint and a single-rigid-link flexible-joint manipulators have been employed. The proposed controllers have been experimentally tested for different trajectories, velocities and several flexibilities of the joints. This ensures that the controllers are able to perform effectively at different trajectories and speeds. Besides developing control strategies for the flexible-joint manipulators, dynamic modeling and vibration suppression of flexible-link manipulators are other parts of this study. To derive dynamic equations for the flexible-link flexible-joint manipulators, the Lagrange method is used. The simulation results from Lagrange method are then confirmed by the finite element analysis (FEA) for different trajectories. To suppress the vibration of flexible manipulators during the manoeuvre, a collocated sensor-actuator is utilized, and a proportional control method is employed to adjust the voltage applied to the piezoelectric actuator. Based on the controllability of the states and using FEA, the optimum location of the piezoelectric along the manipulator is found. The effect of the controller’s gain and the delay between the input and output of the controller are also analyzed through a stability analysis

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

Adaptive Control of Flexible Joint Robots Derived from Arm Energy Considerations

Almost all industrial robots exhibit joint flexibility due to mechanical compliance of their gear boxes. In this paper we outline a design of an adaptive controller for flexible joint robots based on the arms energy. The desired actuator trajectory in a flexible joint robot is dependent not only on the desired kinematic trajectory of the link but also on the link dynamics. Unfortunately, link dynamic parameters are unknown in most cases, as a result the desired actuator trajectory is also unknown. To overcome this difficulty, a number of control schemes have suggested the use of acceleration and link jerk feedback. In this paper we describe a control scheme which does not use link jerk or acceleration. The control law we derive is based on the energy of the arm deviating from the desired trajectory and it has two stages with two corresponding adaptation laws. The first stage drives the actuator and the joints to a desired manifold, the second controller then seeks to drive the joints to their desired trajectory. On application of our first controller there is an apparent structural reduction of the order of the system. This apparent reduction in the structure is exploited by our second stage controller. Our control scheme does not require link acceleration or jerk measurements, and the numerical differentiation of the velocity signal, or the inversion of the inertial matrices are also unnecessary. Simulations are presented to verify the validity of the control scheme. The superiority of the proposed scheme over existing rigid robot adaptive schemes is also illustrated through simulation

Composite computed torque control of robots with elastic motor transmission

The main problem in the control of robots with elastic transmissions between the actuators and the rigid links is caused by the number of control inputs being less than the number of degrees of freedom. This problem has been faced by a composite control law consisting of the conventional `rigid' computed torque controller for link-based trajectory tracking and a `flexible' computed torque part multiplicated with the inverse of the stiffness matrix for stabilization of the elastic deflections. The resultant control system resembles the so-called two-time scale sliding control technique of Slotine and Hong (1987), but in the authors approach the stiffnesses of the elastic motor transmissions do not have to be relatively large neither is there the restriction that there have to be as many motor inputs as elastic transmissions. The goal of the composite controller is that the individual link trajectories will follow the desired trajectories while the elastic-transmission forces/torques, which are not directly constrained by the output specifications, remain on a certain `manifold' due to the natural flexibility behavior of the system. The key concept is illustrated with simulation results of a translation-rotation robot with one torsional-elastic motor transmissio

Sampled-Data Sliding Mode Control Design of Single- Link Flexible Joint Robotic Manipulator

International audienceIn this paper, we have designed a sampled data control law for the single-link flexible joint robotic manipulator using two different approaches. First, we have designed the sampled-data sliding mode control (SMC) based on the continuous time system. In the second approach, we have obtained the approximate discrete model of the system and then designed discrete sliding mode control based on this approximate system. Simulation results have been obtained and a performance comparison has been presented for both techniques

Optimal integral sliding mode controller controller design for 2-RLFJ manipulator based on hybrid optimization algorithm

A newly hybrid nature-inspired algorithm called HSSGWOA is presented with the combination of the salp swarm algorithm (SSA) and grey wolf optimizer (GWO). The major idea is to combine the salp swarm algorithm's exploitation ability with the grey wolf optimizer's exploration ability to generate both variants' strength. The proposed algorithm uses to tune the parameters of the integral sliding mode controller (ISMC) that design to improve the dynamic performance of the two-link flexible joint manipulator. The efficiency and the capability of the proposed hybrid algorithm are evaluated based on the selected test functions. It is clear that when compared to other algorithms like SSA, GWO, differential evolution (DE), gravitational search algorithm (GSA), particles swarm optimization (PSO), and whale optimization algorithm (WOA). The ISMC parameters were tuned using the SSA, which was then compared to the HSSGWOA algorithm. The simulation results show the capabilities of the proposed algorithm, which gives an enhancement percentage of 57.46% compared to the standard algorithm for one of the links, and 55.86% for the other

Extended grey wolf optimization–based adaptive fast nonsingular terminal sliding mode control of a robotic manipulator

This article proposes a novel hybrid metaheuristic technique based on nonsingular terminal sliding mode controller, time delay estimation method, an extended grey wolf optimization algorithm and adaptive super twisting control law. The fast convergence is assured by nonsingular terminal sliding mode controller owing to its inherent nonlinear property and no prior knowledge of the robot dynamics is required due to time delay estimation. The proposed extended grey wolf optimization algorithm determines an optimal approximation of the inertial matrix of the robot. Moreover, adaptive super twisting control based on the Lyapunov approach overcomes the disturbances and compensate the higher dynamics not achievable by the time delay estimation method. First, the fast nonsingular terminal sliding mode controller relying on time delay estimation is designed and is combined with super twisting control for chattering attenuation. The constant gain matrix of the time delay is determined by the proposed extended grey wolf optimization algorithm. Second, an adaptive law based on Lyapunov stability theorem is designed for improving tracking performance in the presence of uncertainties and disturbances. The novelty of the proposed method lies in the adaptive law where the prior knowledge of parametric uncertainties and disturbances is not needed. Moreover, the constant gain matrix of time delay estimation method is obtained using the proposed algorithm. The control method has been tested in simulation on a 3-degrees of freedom robotic manipulator in trajectory tracking mode in the presence of control disturbances and uncertainties. The results obtained confirmed the effectiveness, robustness and the superior precision of the proposed control method compared to the classical ones

Simple Pole Placement Controller for Elastic Joint Manipulator

This paper presents investigations into the development of simple pole placement controller for tip angular position tracking and deflection reduction of an elastic joint manipulator system. A Quanser elastic joint manipulator is considered and the dynamic model of the system is derived using the Euler-Lagrange formulation. The pole placement controller is designed based on integral state feedback structure and the feedback gain is computed based on the desired time response specifications of tip angular position. The proposed control scheme is also compared with a hybrid Linear Quadratic Regulator (LQR) with input shaper control scheme. The performances of the control schemes are assessed in terms of tip angular tracking capability, level of deflection angle reduction and time response specifications. Finally, a comparative assessment of the control techniques is presented and discussed