Kineto-elasto-static synthesis of a 3-<Emphasis Type="Underline">C</Emphasis>RU spherical wrist for miniaturized assembly tasks

The article presents the preliminary studies for the prototyping of a spherical parallel robot for miniaturized assembly applications. The closed-form solution of robot’s kinematics allowed to optimize its (rotation) workspace by taking into account all singularity surfaces and the maximum strokes of the linear actuators. Then, in view of flexures design, the maximum rotations of the passive joints have been calculated and finally the design of the legs and of the whole robot has been carried out by means of a FEM software, with due regard to the non-linearities arising from large displacements.     

Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.     

Gravity compensation of parallel kinematics mechanism with revolute joints using torsional springs

Abstract

Passive gravity compensation technologies based on counterweight and torsional springs is rarely discussed due to the unavailability of an exact mathematical manipulation to determine the required spring constants to achieve the static balance. This article proposes using these springs for a parallel kinematics mechanism with revolute joints. Either the spring constants or initial spring displacements are determined by a constrained optimization approach aiming at minimizing the total potential energy of the mechanism or the static reaction in the actuation direction at the actuators, along a prescribed trajectory. This results in reduced actuation forces/ torques and hence reduced power consumption.     

Optimization Problems of Controlled Multibody Systems Having Spring-Damper Actuators

The optimal control of the motion of mechanical systems is studied. A characteristic feature of these systems is the presence of passive actuators (springs, dampers, etc.). Energy-optimal control laws and structural parameters of nonlinear spring–damper actuators are determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. As an example, a numerical solution is presented for the problem of designing an energy-optimal spring actuator for a robot manipulator of closed kinematic structure     

Detumbling strategy and coordination control of kinematically redundant space robot after capturing a tumbling target

This paper focuses on the motion planning to detumble and control of a space robot to capture a non-cooperative target satellite. The objective is to construct a detumbling strategy for the target and a coordination control scheme for the space robotic system in post-capture phase. First, the dynamics of the kinematically redundant space robot after grasping the target is presented, which lays the foundation for the coordination controller design. Subsequently, optimal detumbling strategy for the post-capture phase is proposed based on the quartic B\(\acute{\text{ e }}\)zier curves and adaptive particle swarm optimization algorithm subject to the specific constraints. Both detumbling time and control torques were taken into account for the generation of the optimal detumbling strategy. Furthermore, a coordination control scheme is designed to track the designed reference path while regulating the attitude of the chaser to a desired value. The space robot successfully dumps the initial velocity of the tumbling satellite and controls the base attitude synchronously. Simulation results are presented for detumbling a target with rotational motion using a seven degree-of-freedom redundant space manipulator, which demonstrates the feasibility and effectiveness of the proposed method.     

Disturbance compensation of a dual-arm underwater robot via redundant parallel mechanism theory

Disturbance compensation is one of the major issues for underwater robots to hover as a mobile platform and to manipulate an object in an underwater environment. This paper presents a new strategy of disturbance compensation for a mobile dual-arm underwater robot using internal torques derived from redundant parallel mechanism theory. A model of the robot was analyzed by redundant serial and parallel mechanisms at the same time. The joint torque to operate the robot is obtained from a redundant serial mechanism model with null-space projection due to redundancy. The joint torque derived from the redundant parallel kinematic model is calculated to perfectly compensate for disturbances to the mobile platform and is included in the solution of the joint torque based on the serial redundant model. The resultant joint torque can generate force on the end-effector for required tasks and forces for disturbance compensation simultaneously . A simulation shows the performance of this disturbance compensation strategy. The joint torque based on the algorithm generates the desired task force and the disturbance compensation force together, and a little additional joint torque can generate a large internal force effectively due to the characteristics of a redundant parallel mechanism. The proposed method is more effective than compensation methods using thrusting force on the mobile platform.     

Kinematic analysis of multi-loop spatial mechanisms: The five-loop case

Multi-loop spatial mechanisms, or parallel mechanisms, are being used to an increasing degree in robotic applications, because they offer some advantages over the open-chain mechanisms. In fact they exhibit high stiffness and low inertia, a fair compliance to the design requirements, and the ability to hold the power actuators in the base. On the other hand, they are often so complex that they can be analyzed only by digital computers, and in general they are designed on the basis of practical solutions rather than theoretical investigations of their structure and kinematics.This paper on the kinematic analysis of multi-loop spatial mechanisms deals in particular with manipulators with five loops and lower pairs. Two approaches are outlined, according to the different backgrounds of the authors: the decomposition method [9], and a differential approach to the non-linear equation set, 19.(6) which encompasses the direct and inverse kinematic problems, as well as the synthesis of the robot.The results are then specialized for mechanisms with the end-effector supported by three spatial parallelograms, like the DELTA-4 robot. For this class of mechanisms an interesting property is also demonstrated, which dramatically reduces the need for computation in the kinematic problems.

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Sommario I meccanismi spaziali in catena chiusa, o meccanismi paralleli, trovano sempre più largo impiego in robotica, dal momento che presentano taluni vantaggi rispetto ai meccanismi in catena aperta: offrono tra l'altro elevata rigidezza e bassa inerzia, flessibilità nel soddisfare le esigenze progettuali e possibilità di collocare gli azionamenti nella base. Spesso tuttavia la loro complessità è tale che si possono analizzare solo col computer, e vengono quindi progettati a partire da soluzioni pratiche, piuttosto che da sistematiche basi teoriche. Questo lavoro illustra metodi generali per lo studio cinematico di meccanismi spaziali in catena chiusa, riferendoli al caso di meccanismi con cinque catene e coppie cinematiche elementari. Gli approcci presentati, che riflettono la diversa formazione degli autori, sono: un metodo di decomposizione [9], e un metodo basato sul calcolo differenziale per lo studio del sistema di equazioni non lineari (6) che, in forma implicita, configura i problemi cinematici diretto e inverso e la sintesi del robot.I risultati vengono quindi applicati a un meccanismo il cui elemento terminale è sostenuto da tre parallelogrammi articolati spaziali, come nel caso del robot DELTA-4. Per questa classe di meccanismi si dimostra anche un'interessante proprietà che riduce drasticamente la quantità di calcoli richiesti dal problema cinematico.

     

Mathematical Modeling, Control, Computer Simulation and Laboratory Experiments of a Spatial Servopneumatic Parallel Robot

In this paper, the special construction of a parallel robot, called spatial servopneumatic multi-axis test facility, will be discussed. The investigations include the following aspects: (i) the laboratory set-up of the robot, (ii) various results obtained in laboratory experiments, taking into account quite different control algorithms and command-input signals, (iii) a comparison of the laboratory experiments with the computer simulations of Part I of this paper, and ({vi}) a quality check of the results compared with the cost of the different controller realizations. The results of both the computer simulations and the laboratory experiments show: (i) The dynamic behavior of the parallel structure can be tremendously improved by using sophisticated nonlinear control algorithms. (ii) This improvement has to be paid by a drastically increased amount of work for deriving the model equations and control algorithms, and by augmented hardware cost of the sensing elements and controller electronics. (iii) Carefully developed model equations and identified model parameters provide theoretical models of the complex parallel structure that are very close to reality. This enables the design engineer to systematically investigate constructive alternatives of the design parameters, sensor and actuator concepts, and control strategies of the MAP prior to their hardware realization.This work has been supported by the German Science Foundation (DFG) under Contract No. Ha 1666/6-3.     

Design of a single motor,tendon driven redundant manipulator with reduced driving joint torques

Lightweight manipulator design is one of the diverse and rich research fields in the area of robotics. It has become increasingly important to develop manipulators with reduced cost, high energy e?ciency and with low inertia. There are numerous design concepts proposed in the past decades such as designing lightweight joints or locating the actuators at the base. Reduction of number of actuators used has added advantages such as cost reduction, reduced power consumption, compact in design apart from reduction of weight. This paper presents a lightweight tendon drive redundant manipulator design with reduced joint torque using a single motor. The proposed design has reduced the number of actuators used. Thus the design is not only effective in reducing driving joint torques but also minimizes the number of actuators required and the power consumption. Driving joint torques computed for both conventional and for the proposed manipulator design highlight the significance of the proposed manipulator.     

Inverse dynamics of the HALF parallel manipulator with revolute actuators

Recursive matrix relations for kinematics and dynamics of the HALF parallel manipulator are presented in this paper. The prototype of this robot is a spatial mechanism with revolute actuators, which has two translation degrees of freedom and one rotation degree of freedom. The parallel manipulator consists of a base plate, a movable platform and a system of three connecting legs, having wide application in the fields of industrial robots, simulators, parallel machine tools and any other manipulating devices where high mobility is required. Supposing that the position and the motion of the moving platform are known, an inverse dynamics problem is solved using the principle of virtual powers. Finally, some iterative matrix relations and graphs of the torques and powers for all actuators are analysed and determined. It is shown that this approach is an effective means for kinematics and dynamics modelling of parallel mechanisms.     

Treadmill walking of the pneumatic biped Lucy: Walking at different speeds and step-lengths

Actuators with adaptable compliance are gaining interest in the field of legged robotics due to their capability to store motion energy and to exploit the natural dynamics of the system to reduce energy consumption while walking and running. To perform research on compliant actuators we have built the planar biped Lucy. The robot has six actuated joints, the ankle, knee and hip of both legs with each joint powered by two pleated pneumatic artificial muscles in an antagonistic setup. This makes it possible to control both the torque and the stiffness of the joint. Such compliant actuators are used in passive walkers to overcome friction when walking over level ground and to improve stability. Typically, this kind of robots is only designed to walk with a constant walking speed and step-length, determined by the mechanical design of the mechanism and the properties of the ground. In this paper, we show that by an appropriate control, the robot Lucy is able to walk at different speeds and step-lengths and that adding and releasing weights does not affect the stability of the robot. To perform these experiments, an automated treadmill was built Published in Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 134–142, July 2008.     

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close.     

Penalty Methods for Numerical Approximations of Optimal Boundary Flow Control Problems

Abstract

This article is concerned with penalty methods for solving optimal Dirichlet control problems governed by the steady-state and time-dependent Navier-Stokes equations. We present, in two different versions, the penalized methods for solving the steady-slate Dirichlet control problems. These approaches are implemented and compared numerically. We also generalize the penalty methods to the time-dependent case. Scmidiscrete and fully discrete approximations of time-dependent Dirichlet control problems are discussed and implemented. Numerical results for solving both the steady-state and the time dependent Dirichlet control problems are reported.     

Full-order optimal compensators for flow control: the multiple inputs case

Flow control has been the subject of numerous experimental and theoretical works. We analyze full-order, optimal controllers for large dynamical systems in the presence of multiple actuators and sensors. The full-order controllers do not require any preliminary model reduction or low-order approximation: this feature allows us to assess the optimal performance of an actuated flow without relying on any estimation process or further hypothesis on the disturbances. We start from the original technique proposed by Bewley et al. (Meccanica 51(12):2997–3014, 2016.  https://doi.org/10.1007/s11012-016-0547-3), the adjoint of the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows bypassing the solution of the algebraic Riccati equation associated with the optimal control problem, typically infeasible for large systems. In this numerical work, we extend the ADA iteration into a more general framework that includes the design of controllers with multiple, coupled inputs and robust controllers (\(\mathcal {H}_{\infty }\) methods). First, we demonstrate our results by showing the analytical equivalence between the full Riccati solutions and the ADA approximations in the multiple inputs case. In the second part of the article, we analyze the performance of the algorithm in terms of convergence of the solution, by comparing it with analogous techniques. We find an excellent scalability with the number of inputs (actuators), making the method a viable way for full-order control design in complex settings. Finally, the applicability of the algorithm to fluid mechanics problems is shown using the linearized Kuramoto–Sivashinsky equation and the Kármán vortex street past a two-dimensional cylinder.     

Controlling robot manipulators by dynamic programming

A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems. In this article, we provide a detailed presentation of the mechanical and electrical implications of robots equipped with DC motor actuators. This model takes into account all non-linear aspects of the system. Then, we develop computational algorithms for optimal control based on dynamic programming. The robot's trajectory must be predefined, but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied. As an example, a manipulator arm with 3 degress of freedom is analyzed.     

Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load

Based on the theory of piezoelasticity, a functionally graded piezoelectric sandwich cantilever under an applied electric field and/or a heat load is studied. All materials may be arbitrary functional gradients in the thickness direction. The static solution for the mentioned problems is presented by the Airy stress function method. As a special case, assuming that the material composition varies continuously in the direction of the thickness according to a power law distribution, a comprehensive parametric study is conducted to show the influence of electromechanical coupling (EMC), functionally graded index, temperature change and thickness ratio on the bending behavior of actuators or sensors. The distribution of electric field or normal stress in present FGPM actuators is continuous along the thickness, which overcomes the problem in traditional layered actuators. The solution facilitates the design optimization for different piezoelectric actuators and has another potential application for material parameter identification.     

A note on the “nonlinear control of electrical flexible-joint robots”

Robust tracking control of electrically flexible-joint robots is addressed in this paper. Two important practical situations are considered. The fact that robot actuators have limited voltage and that current measurement is subjected to noise. Let us notice that a few solutions for the voltage-bounded robust tracking control have been proposed. In this paper, we contribute to this subject by presenting a new form of voltage-based control strategy. It proves that the closed loop system is BIBO stable, while actuator/link position errors are uniformly–ultimately bounded stable in agreement with Lyapunov’s direct method in any finite region of the state space. As a second contribution of this paper, we present a robust adaptive control scheme without the need for computation of regressor matrix and current measurement, with the same result on the closed loop system stability. This novelty gives a simple robust tracking control scheme for both structured and unstructured uncertainties based on the function approximation technique. The analytical studies as well as experimental results produced using MATLAB/Simulink external mode control on a flexible-joint electrically driven robot demonstrate high performance of the proposed control scheme.

     

Analytical Treatment of Some Extended Problems in Structural Optimization,Part I

ABSTRACT

Optimization problems involving supports of unspecified location as well as variable external actions and reactions of nonzero cost are discussed in the context of both plastic and elastic beams and frames, of non-preassigned, partially preassigned, and preassigned cost distribution, and of strength or deflection constraints.

The static-kinematic optimality criteria for various classes of problems are illustrated with simple examples and the results are checked by an independent method, i.e., by differentiation of the total cost with respect to the unknown variables. It is shown that for certain classes of problems the conditions introduced reduce to existing criteria by Prager and Masur.     

Maneuvering Aspects and 3D Effects of Active Airfoil Flow Control

An active flow control experiment was conducted on a cropped NACA 0018 airfoil to study 3D effects and maneuverability aspects made possible by a segmented actuation system installed in the airfoil. The 14 piezo-fluidic actuators were installed at the corner of the cropped region, inclined at 30° to the local surface, facing downstream. Operating all actuators at unison significantly increased lift and generated a pitch-down moment. Operating all actuators at the same magnitude but varying the phase along the span generated larger lift-increment, with respect to the uniform phase excitation. Significant rolling moment can be generated when only half-span of the wing is actuated. The latter effect, as indicated by the 3D pressure distribution, persists to the leading edge even though the excitation was introduced close to the trailing edge. When a pair, out of the possible fourteen actuators is not operating, very little of the control authority is lost. This is an important finding when issues like fault tolerance and robustness of fluidic-piezo actuators are considered.