Adaptive control of robot manipulators with flexible joints

Presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value, i.e., the results are not restricted to weak joint elasticity. Moreover, the joint flexibility is not assumed to be known. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded     

A systematic formulation of dynamic equations for robot manipulators with elastic links

Although a variety of formulation schemes for the dynamic equations of robot manipulators with rigid links can be found in the literature, an efficient method of the formulation for robot manipulators with elastic links is not well known. Accordingly, this work presents the derivation of the equations of motion for application to mechanical manipulators with elastic links. The formulation is conducted analytically using Hamilton's principle. The resultant equations consist of the terms of inertial, Coriolis, centrifugal, gravitational, and exerted forces. They are expressed in terms of a set of independent generalized coordinates. In contrast to conventional variational approaches, the present method provides an efficient and systematic way for obtaining the compact symbolic equations of flexible manipulator systems. Two examples are presented to illustrate the proposed methodology. Firstly, a three-link flexible manipulator with three revolute joints is studied. A flexible manipulator consisting of a prismatic joint and a discrete mass is the second model.     

An observer-based set-point controller for robot manipulators with flexible joints

We present a globally asymptotically stable controller for point-to-point regulation of robot manipulators with flexible joints that uses only position measurement on the motor side. Existing asymptotically stable schemes for the set point regulation problem without velocity measurement address only the rigid robot case. Furthermore, these solutions ensure only local stability provided some bounds on the dynamic part of the robot model are known. Also, they require the injection of high gains into the loop to enlarge the equilibrium domain of attraction. In contrast, our solution is global, applies for robots with flexible joints and assumes only that the gravity forces are known. The underlying rationale of the design is to ‘shape’ the potential energy of the closed loop system so that it has an absolute minimum at the desired equilibrium, and add the required dampingto achieve asymptotic stability. This is attained by adding a (linear) observer that converges to the position required to compensate the gravity forces and injects the damping, and a ‘spring-like’ effect between the observer and the robot that ‘pulls’ the robot to the desired target. This approach to observer-based controller design differs from the classical certainly equivalent approach and effectively exploits the dynamic properties of the physical system.     

Inverse dynamics based robust control method for position commanded servo actuators in robot manipulators

In this paper, a simple torque to position conversion method is proposed for position commanded servo actuators used in robot manipulators. The torque to position conversion is based on the low level controller of the servomotor. The proposed conversion law is combined with a backstepping sliding mode control method to realize a robust dynamic controller. The proposed torque based method can control a servomotor which can otherwise be operated only through position inputs. This method facilitates dynamic control for position controlled servomotors and it can be extended to position commanded robotic manipulators also. Simulation and experimental studies are conducted to validate the proposed torque to position conversion based robust control method.     

A geometric optimization method for the trajectory planning of flexible manipulators

Multibody System Dynamics - Lightweight and flexible robots offer an interesting answer to industrial needs for safety and efficiency. The control of such systems should be able to deal properly...     

A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints

In the present study, for the first time, flexible multibody dynamics for a three-link serial robot with two flexible links having active prismatic joints is presented using an approximate analytical method. Transverse vibrations of flexible links/beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the links. In this study, first, vibration analysis of a flexible link sliding through an active prismatic joint having translational motion is considered. A rigid-body coordinate system is used, which aids in obtaining a new and rather simple form of the kinematic differential equation without the loss of generality. Next, the analysis is extended to include dynamic forces for a three-link planar serial robot called PPP (Prismatic, Prismatic, Prismatic), in which all joints are prismatic and active. The robot has a rigid first link but flexible second and third links. To model the prismatic joint, time-variant constraints are written, and a motion equation in a form of virtual displacement and virtual work of forces/moments is obtained. Finally, an approximate analytical method called the “constrained assumed modes method” is presented for solving the motion equations. For a numerical case study, approximate analytical results are compared with finite element results, which show that the two solutions closely follow each other.     

A low-level control interface for robot manipulators

This paper will discuss a possible low-level control interface for a robot manipulator. The first section will present background information describing the capabilities and limitations afforded by the use of interfaces and a proposed system modularization that supports interface specification. The next section presents three possible low-level robot control interfaces within this system. Each will be elaborated on by a specification of the interface information and its use, timing considerations and potential limitations. The paper concludes with a summary discussion and recommendation.     

A multivariable control scheme for robot manipulators

The article puts forward a simple scheme for multivariable control of robot manipulators to achieve trajectory tracking. The scheme is composed of an inner loop stabilizing controller and an outer loop tracking controller. The inner loop utilizes a multivariable PD controller to stabilize the robot by placing the poles of the linearized robot model at some desired locations. The outer loop employs a multivariable PID controller to achieve input-output decoupling and trajectory tracking. The gains of the PD and PID controllers are related directly to the linearized robot model by simple closed-form expressions. The controller gains are updated on-line to cope with variations in the robot model during gross motion and for payload change. Alternatively, the use of high gain controllers for gross motion and payload change is discussed. Computer simulation results are given for illustration.     

A globally convergent adaptive controller for robot manipulators

In this work, a globally convergent adaptive scheme is developed for controlling robot manipulators. Asymptotic behavior of the tracking error is established using the properties of the robot dynamics. A modified version of the controller which employs the filtered torque in its update law is also shown to have the same convergence properties     

A discrete-time adaptive control scheme for robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.     

A robust neural controller for underwater robot manipulators

Presents a robust control scheme using a multilayer neural network with the error backpropagation learning algorithm. The multilayer neural network acts as a compensator of the conventional sliding mode controller to improve the control performance when initial assumptions of uncertainty bounds of system parameters are not valid. The proposed controller is applied to control a robot manipulator operating under the sea which has large uncertainties such as the buoyancy, the drag force, wave effects, currents, and the added mass/moment of inertia. Computer simulation results show that the proposed control scheme gives an effective path way to cope with those unexpected large uncertainties.     

On the robust control of robot manipulators including actuator dynamics

A robust nonlinear control law that incorporates the manipulator dynamics as well as dynamics of actuators is developed in this article. The inertial parameters of the manipulator and the electrical parameters of the actuators are considered to be of uncertain values. In contrast to the known methods, the presented design procedure is based on less restrictive assumptions regarding the characteristics of uncertainties. We just assume that unknown parameters are bounded, which is evidently true for any robotic system. Exponential stability of the developed controller is proved by the Lyapunov method. © 1996 John Wiley & Sons, Inc.     

Flexible control for robot manipulators

We designed, implemented, and tested a real-time flexible controller for manipulating different types of robots and control algorithms. The robot-independent, IBM PC-based multiprocessor system contains a DSP56001 master controller, six independent HCTL-1100 joint processors for accurate robotic joint control, and an interface computer board for processor communication. The joint processors operate in four user-defined modes and can be connected directly to an incremental optical encoder, which accommodates specialized applications and eliminates extra hardware     

Finite-time control for robot manipulators

Finite-time control of the robot system is studied through both state feedback and dynamic output feedback control. The effectiveness of the proposed approach is illustrated by both theoretical analysis and computer simulation. In addition to offering an alternative approach for improving the design of the robot regulator, this research also extends the study of the finite-time control problem from second-order systems to a large class of higher order nonlinear systems.     

Fault identification for robot manipulators

Several factors must be considered for robotic task execution in the presence of a fault, including: detection, identification, and accommodation for the fault. In this paper, a nonlinear observer is used to identify a class of actuator faults once the fault has been detected by some other method. Advantages of the proposed fault-identification method are that it is based on the nonlinear dynamic model of a robot manipulator (and hence, can be extended to a number of general Euler Lagrange systems), it does not require acceleration measurements, and it is independent from the controller. A Lyapunov-based analysis is provided to prove that the developed fault observer converges to the actual fault. Experimental results are provided to illustrate the performance of the identification method.     

Constrained motion control of flexible robot manipulators based on recurrent neural networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.     

A class of nonlinear PD-type controllers for robot manipulators

In this article we present the stability analysis of a class of PD-type controllers for position and motion control of robot manipulators. The main feature of this class of controllers is that the proportional and derivative gains can be nonlinear functions of the robot states. These controllers can be obtained from control strategies that adjust the controller gains depending on the robot states. It is shown that global asymptotic stability of the control system is achieved provided that the P and D gains have suitable structure. As an outcome, we propose a global regulator constrained to deliver torques within prescribed limits of the actuator's capabilities. Experimental results on a two degrees of freedom direct drive arm show the usefulness of the proposed scheme. © 1996 John Wiley & Sons, Inc.     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

Robust controller design for a class of nonlinear robot manipulators with actuator dynamics

A robust controller is proposed to achieve accurate tracking for a class of nonlinear uncertain robot manipulators with actuator dynamics. A dynamic model is derived that incorporates the manipulator dynamics with the actuator dynamics. The parameter uncertainty in the model is quantified using the linear parameterization technique. The proposed switching controller guarantees the global asymptotic stability. To rectify the chattering caused by the switching action of the controller, the controller is modified into a smoothed form by putting a boundary layer around the sliding surface. It is shown that the smoothing controller guarantees the uniform ultimate boundedness of the actual trajectory. Simulation results show the feasibility and excellent tracking performance of the controller.     

The path precompensation method for flexible arm robot

This paper constructed a closed loop path precompensation method for a flexible arm robot. A torque computation method taking care of the elastic arm deformation was first proposed and discussed. A concept of partial deformation compensation was subsequently proposed to improve the torque profiles and the trajectory fidelity. The advantage of this concept was first shown by examples of planar trajectory. After the construction of the closed-loop path precompensation method for a flexible arm, the torque method and partial deformation compensation were incorporated to track the spatial trajectory. Numerical simulations were given to show the usefulness of the proposed concept and method.