Pathplanning and control of an autonomous robot vehicle with a manipulator

An autonomous mobile robot is presented. It consists of two parts: a mobile vehicle underneath a robotarm with DOF 5. These two are a nonholomic (the mobile vehicle) and a holonomic subsystem (the robotarm). To give the robot orders or tasks to accomplish this can be done from an external controlsoftware via TCP–IP to the controlsoftware of the robot. An embedded system involves chart creation, pathplanning (global, local), evaluation of sensorsignals, object– and/or marker–detection and a controlled movement. Futhermore it communicates over FIFOs with an nonrealtime–task which allows a communication via TCP–IP. Several sensors are implemented, e.g. infrared–/ ultrasonic–range sensors connected via CAN to the embedded board, as well as the control boards for each engine. A Laserscanner is installed in front of the robot to detect edges and obstacles. For marker–tracking and object recognition an USB–Webcam is added on the robotarm. For avoidance of collisions between the robotarm and the mobile robot a repeller is introduced. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analysis of controlled multiple-link robotic manipulator systems with time delays

Controlled robotic manipulator systems, normally operating in an acceptable manner, may become unstable, when time delays exist in the feedback loop. This instability may cause oscillations and thus deteriorate the system performance. In this paper we introduce a method to analyze the performance of robotic manipulators with small time delays in the feedback loop. Specifically, we may predict the limits of a stable system Operation, i.e., the robustness and expected system error bounds, as a function of the time delay and system parameters. The analysis method uses nonlinear control theory concepts, such as Lyapunov's second method, and takes advantage of norms to establish operational bounds. Previous research of time-delay systems analysis is also reviewed, in general, and pertaining to robotic controls, in particular. The results of the analysis can be displayed graphically and may be used to adjust the controller gains and trajectories to ensure satisfactory operation. Predictably, the system response is slowed as the time delay increases. The validity of the analysis is demonstrated with a numerical example of a two-link manipulator using a computed-torque controller. The time responses of the example, run on a computer-generated model, supports the analysis results and predicted performance.     

Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint

In this study, mathematical modelling and dynamic response of a flexible robot manipulator with rotating-prismatic joint are investigated. The tip end of the flexible robot manipulator traces a multi-straight-line path under the action of an external driving torque and an axial force. Considered robot manipulator consists of a rotating prismatic joint and a sliding flexible arm with a tip mass. Flexible arm is assumed to be an Euler–Bernoulli beam carrying an end-mass. Equations of motion of the flexible manipulator are obtained by using Lagrange’s equation of motion. Effect of rotary inertia, axial shortening and gravitation is considered in the analysis. Equations of motion are solved by using fourth order Runge–Kutta method. Numerical simulations obtained by using a developed computer program are presented and physical trend of the results are discussed.     

Control concepts for a parallel manipulator with flexible links

Light-weight robots are advantageous considering the low energy consumption and the low material cost. However, in light-weight structures significant oscillations can occur which make the control very challenging. Objective of this research is end-effector trajectory tracking of a parallel manipulator with flexible links. Hereby, only the manipulator's drives are used, and no additional actuation on the flexible bodies is considered. For accurate trajectory tracking, feedforward control of the manipulator is used based on inverse dynamics and servo-constraints, combined with feedback control of the drive positions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping

In this paper, an adaptive fuzzy output feedback approach is proposed for a single-link robotic manipulator coupled to a brushed direct current (DC) motor with a nonrigid joint. The controller is designed to compensate for the nonlinear dynamics associated with the mechanical subsystem and the electrical subsystems while only requiring the measurements of link position. Using fuzzy logic systems to approximate the unknown nonlinearities, an adaptive fuzzy filter observer is designed to estimate the immeasurable states. By combining the adaptive backstepping and dynamic surface control (DSC) techniques, an adaptive fuzzy output feedback control approach is developed. Stability proof of the overall closed-loop system is given via the Lyapunov direct method. Three key advantages of our scheme are as follows: (i) the proposed adaptive fuzzy control approach does not require that all the states of the system be measured directly, (ii) the proposed control approach can solve the control problem of robotic manipulators with unknown nonlinear uncertainties, and (iii) the problem of “explosion of complexity” existing in the conventional backstepping control methods is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Modelling and control of a Puma-like manipulator

This work deals with the modelling and control of a Puma-like manipulator. A control problem concerning the motion of the manipulator's end-effector in the half space {(x, y, z) : z ⪢ H}, H ⪢ 0, is dealt with. The problem is solved by first using an inverse dynamics transformation, and then by minimizing a penalty function.     

Modeling and nonlinear control of a flexible-link manipulator

The problem of modeling and controlling the tip position of a one-link flexible manipulator is considered. The proposed model has been used to investigate the effect of the open-loop control torque profile, and the payload. The control strategy is based on the nonlinear State Dependent Riccati Equation (SDRE) design method in the context of application to robotics and manufacturing systems. In this paper, an experimental test-bed was developed to demonstrate the concept of end-point position feedback on a single-link elastic manipulator, and the control strategy for a single-link flexible manipulator. The controller is designed based on the nonlinear SDRE developed by the authors and applied to a flexible manipulator. The experimental results are compared with conventional PD controller strategy. The results reveal that the nonlinear SDRE controller is near optimal and robustly; and its performance is improved comparing to the PD control scheme.     

Simulation and feed-forward control of a flexible parallel manipulator

The importance of lightweight constructions are steady increasing since they promise a low energy consumption together with higher movement speeds. However these demand modern, model-based feed-forward control designs. Especially the undesired vibrations due to the reduced overall stiffness of such manipulators have to be taken into account. A convenient way to model the dynamical behavior of systems that perform large, nonlinear motions superposed with small, elastic deformations is the floating frame of reference approach in a flexible multibody system. The application of the Newton-Euler-Formalism together with D'Alembert's principle to parallel manipulators results in a set of differential-algebraic equations. Therefore, the consideration of the trajectory tracking problem with so-called servo constraints appears to be promising. In case of a non-flat system, the arising set of differential-algebraic equations, which consists of the system dynamics, the holonomic loop closing constraint equations and the servo constraints embodies nontrivial dynamics. With an oblique projection, the embedded set of ordinary differential equations describing the internal dynamics can be obtained. The stability properties of these dynamics determines the complexity of the feed-forward control design, as two-point boundary value problems might have to be solved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Switched control of a nonholonomic mobile robot

We present a switched control algorithm to stabilize a car-like mobile robot which possesses velocity level nonholonomic constraint. The control approach rests on splitting the system into several second-order subsystems and then stabilizing the system sequentially using finite-time controllers, finally resulting in the mobile robot being moved from one point to another point. State dependent switching control is employed in which the controllers switches on a thin surface in the state-space. Robustness analysis is presented by redefining the switching signal using relaxed switching surface. Both, non-robust and robust controllers are validated through numerical simulation.     

Dynamic modelling of a rigid-flexible manipulator for constrained motion task control

A mathematical model governing the dynamics of a constrained rigid-flexible manipulator moving in a horizontal plane is derived using Hamilton's principle. A new variable is introduced before the procedure of modal expansion in order to convert the non-homogeneous boundary condition into a homogeneous one. The static tip deflection of the flexible link is allowed in order to maintain the contact force between the end effector and the constrained path and this tip deflection is considered in both the inverse kinematics and the order reduction procedures. The state vector of the proposed controller consists of joint angle of the rigid link, its derivative and integral, the first deflection mode and its derivative, and the integral of contact force. A multivariable controller is proposed for the simultaneous motion and force control of the manipulator. The controller consists of a feedforward term which contributes the torque for the expected joint angles and the contact force, and a feedback term with the time varying optimal gains obtained from the Matrix Riccati equation. Computer simulation results show that this proposed controller is capable of performing the straight line tracking task satisfactorily under four different conditions.     

Intelligent active force control of a 3-RRR parallel manipulator incorporating fuzzy resolved acceleration control

This paper introduces a novel intelligent control scheme for robust and precise positioning and orientation of a class of highly non-linear 3-RRR (revolute-revolute-revolute) planar parallel manipulator. The primary objective is to force the manipulator to track accurately a prescribed Cartesian trajectory when the system is subjected to different types of disturbances in the forms of forced harmonic excitations. A two level fuzzy tuning resolved acceleration control (FLRAC) is first designed and implemented to the system to demonstrate the stable response of the manipulator in performing trajectory tracking tasks in the absence of the disturbances. In this scheme, the first level of fuzzy tuning is used to acquire the proportional-derivative (PD) gains linearly while the second level considers non-linear tuning for determining the other parameters of the fuzzy controller to increase its performance. Then, the controller is added in series with an active force controller (AFC) to create a novel two degree-of-freedom (DOF) controller known as FLRAC-AFC which is subsequently and rigorously tested for system robustness and accuracy in tracking the prescribed trajectory. The simulation study provides further insight into the potentials of the proposed robotic system in rejecting the disturbances for the given operating conditions. The results clearly show that the FLRAC-AFC scheme provides a much superior trajectory tracking capability compared to the conventional linear RAC alone.     

Modelling,simulation and control of a redundant parallel robotic manipulator based on invariant manifolds

In this article a systematic approach of modelling and control for a parallel robotic manipulator is presented. Regarding the framework of structured analysis of dynamical systems the derivation of a differential-algebraic model of the mechanical system is straightforward. Using some differential-geometric considerations based on invariant manifolds and the definition of fictitious additional input and output variables a suitable state feedback can be constructed which transforms the differential-algebraic representation into a state-space model for the robotic manipulator. On this basis a classical two-degree-of-freedom (2-DOF) control structure has been designed using the well-known input–output linearization and a linear time-variant Kalman filter-based output feedback. Finally, the control structure including a friction compensation is applied to the robotic system in the laboratory which shows the practical applicability of the proposed procedure.     

Robust control of a spatial robot using fuzzy sliding modes

In order to improve the performance of the sliding mode controller, fuzzy logic sliding mode controller is proposed in this study. The control gain of the conventional sliding mode controller is tuned by a fuzzy logic rule base and, also dynamic sliding surfaces are obtained by changing their slopes using the error states of the system in another fuzzy logic algorithm. These controllers are then combined in order to enhance the performance. Afterwards, proposed controllers were used in trajectory control of a three degrees of freedom spatial robot, which is subjected to noise and parameter variations. Finally, the controllers introduced are compared with a PID controller which is commonly used for control of robotic manipulators in industry. The results indicate the superior performance of the proposed controller.     

Mathematical modeling and fuzzy control of a flexible-link robot arm

In this paper, the Timoshenko theory is applied to investigate a new mathematical model for the “shoulder-elbow-like” single flexible-link robot arm with dampings. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. A new design of a fuzzy-logic-based (PI + D)² control scheme is developed for both vibration suppression and set-point tracking. Computer simulation results for the modeling are performed to observe the significant vibration modes, and simulation results for the control scheme demonstrate that the controllers perform very well for the tracking based on this flexible-link model. A newly developed method for stability analysis using the “two-straight-lines” criterion is also presented.     

Modelling the motion of a three-link manipulator based on a plane with a time-dependent inclination

This work deals with the modelling of a three-link manipulator mounted on a plane with a time-dependent inclination. Two cases are considered.

• (i)The plane is part of a rigid body.
• (ii)The plane is in a moored ship.

     

An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints

To solve disturbances, nonlinearity, nonholonomic constraints and dynamic coupling between the platform and its mounted robot manipulator, an adaptive sliding mode controller based on the backstepping method applied to the robust trajectory tracking of the wheeled mobile manipulator is described in this article. The control algorithm rests on adopting the backstepping method to improve the global ultimate asymptotic stability and applying the sliding mode control to obtain high response and invariability to uncertainties. According to the Lyapunov stability criterion, the wheeled mobile manipulator is divided into several stabilizing subsystems, and an adaptive law is designed to estimate the general nondeterminacy, which make the controller be capable to drive the trajectory tracking error of the mobile manipulator to converge to zero even in the presence of perturbations and mathematical model errors. We compare our controller with the robust neural network based algorithm in nonholonomic constraints and uncertainties, and simulation results prove the effectivity and feasibility of the proposed method in the trajectory tracking of the wheeled mobile manipulator.     

Adaptive anti control of chaos for robot manipulators with experimental evaluations

Roughly speaking, anti control of chaos consists in injecting a chaotic behavior to a system by means of a control scheme. This note introduces a new scheme to solve the anti control of chaos for robot manipulators. The proposed controller uses an adaption law to estimate the robot parameters on line. Thus, the controller does not require any knowledge of the physical parameters of the manipulator, such as masses, lengths of the links, moments of inertia, etc. The new scheme is based in the velocity field control paradigm, hence the specification of a chaotic system to define a desired velocity field is required. Experimental results in a two degrees-of-freedom direct-drive robot illustrate the practical feasibility of the introduced theory. In order to achieve anti control of chaos of our experimental system, two different chaotic attractors are used: the Genesio-Tesi system and a Jerk-type system. Results showed that the controller is able to inject the chaotic behavior to the robot while the robot parameters are estimated on line.     

An estimate of the attraction domain with a specified exponential stability index in a wheeled robot control problem

The problem of synthesizing a law for the control of the plane motion of a wheeled robot is investigated. The rear wheels are the drive wheels and the front wheels are responsible for the turning of the platform. The aim of the control is to steer a target point to a specified trajectory and to stabilize the motion along it. The trajectory is assumed to be specified by a smooth curve. The actual curvature of the trajectory of the target point, which is related to the angle of rotation of the front wheels by a simple algebraic relation, is considered as the control. The control is subjected to bilateral constraints by virtue of the fact that the angle of rotation of the front wheels is limited. The attraction domain in the distance to trajectory - orientation space, is investigated for the proposed control law. Arrival at a trajectory with a specified exponential stability index is guaranteed in the case of initial conditions belonging to the given domain. An estimate of the attraction domain in the form of an ellipse is given.     

Discrete concepts for elliptic optimal control problems with constraints on the gradient of the state

We consider elliptic optimal control problems with constraints on the gradient of the state and propose two distinguish concepts for their discretization. The first concept uses piecewise linear, continuous finite element Ansatz functions for the state, while the second concept uses the lowest order Raviart–Thomas mixed finite element. In both cases variational discretization from [5] is used for the controls. We present optimal finite element error estimates for the numerical solutions and confirm our theoretical findings by a numerical experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)