Iterative Machine Learning for Precision Trajectory Tracking with Series Elastic Actuators

When robots operate in unknown environments small errors in postions can lead to large variations in the contact forces, especially with typical high-impedance designs. This can potentially damage the surroundings and/or the robot. Series elastic actuators (SEAs) are a popular way to reduce the output impedance of a robotic arm to improve control authority over the force exerted on the environment. However this increased control over forces with lower impedance comes at the cost of lower positioning precision and bandwidth. This article examines the use of an iteratively-learned feedforward command to improve position tracking when using SEAs. Over each iteration, the output responses of the system to the quantized inputs are used to estimate a linearized local system models. These estimated models are obtained using a complex-valued Gaussian Process Regression (cGPR) technique and then, used to generate a new feedforward input command based on the previous iteration's error. This article illustrates this iterative machine learning (IML) technique for a two degree of freedom (2-DOF) robotic arm, and demonstrates successful convergence of the IML approach to reduce the tracking error.Comment: 9 pages, 16 figure. Submitted to AMC Worksho

A Specific Methodology of Creep Compensation for piezoelectric Actuators by Open-loop control

Piezoelectric actuators exhibit creep behavior in open-loop operation, which may lead to unaffordable errors in high precision static positioning systems. An inversion-based compensation strategy by open-loop control is presented for reducing creep effect. The approach utilizes a nonlinear viscoelastic model to portray creep phenomenon, which consists of a linear spring, a nonlinear dashpot and a series of nonlinear Voigt elements. It is shown that for the presented creep model the step responses are very similar to the piezoelectric actuators. In order to compensate creep effect, a concept of voltage relaxation in piezoelectric actuators is proposed. And the voltage relaxation model tantamount to the inverse creep model is derived using a PID closed-loop control system. Experimental results prove that, by insertion of voltage relaxation model in open-loop operation, creep effect is attenuated markedly in piezoelectric actuators

Research in structures, structural dynamics and materials, 1989

Topics addressed include: composite plates; buckling predictions; missile launch tube modeling; structural/control systems design; optimization of nonlinear R/C frames; error analysis for semi-analytic displacement; crack acoustic emission; and structural dynamics

Multistable Shell Structures

Multistable structures, which possess by definition more than one stable equilibrium configuration, are capable of adapting their shape to changing loading or environmental conditions and can further improve multi-purpose ultra-lightweight designs. Whilst multiple methods to create bistable shells have been proposed, most studies focussed on free-standing ones. Considering the strong influence of support conditions on related stability thresholds, surprisingly little is known about their influence on multistable behaviour. In fact, the lack of analytical models prevents a full understanding and constitutes a bottle-neck in the development process of novel shape-changing structures. The relevance becomes apparent in a simple example: whilst an unsupported sliced tennis ball can be stably inverted without experiencing a reversion, fixing its edge against rotation erodes bistability by causing an instantaneous snap-back to the initial configuration. This observation reveals the possibility to alter the structural response dramatically by a simple change of the support conditions. This dissertation explores the causes of this behaviour by gaining further insight into the promoting and eschewing factors of multistability and aims to point out methods to exploit this feature in optimised ways. The aforementioned seemingly simple example requires a geometrically nonlinear perspective on shells for which analytical solutions stay elusive unless simplifying assumptions are made. In order to captures relevant aspects in closed form, a novel semi-analytical Ritz approach with up to four degrees of freedom is derived, which enforces the boundary conditions strongly. In contrast to finite element simulations, it does not linearise the stiffness matrix and can thus explore the full solution space spanned by the assumed polynomial deflection field. In return, this limits the method to a few degrees of freedom, but a comparison to reference calculations demonstrated an excellent performance in most cases. First, the level of influence of the boundary conditions on the critical shape for enabling a bistable inversion is formally characterised in rotationally symmetric shells. Systematic insight is provided by connecting the rim to ground through sets of extensional and rotational linear springs, which allows use of the derived shell model as a macro-element that is connected to other structural elements. It is demonstrated that bistability is promoted by an increasing extensional stiffness, i.e. bistable roller-supported shells need to be at least twice as tall compared to their fixed-pinned counterparts. The effect of rotational springs is found to be multi-faceted: whilst preventing rotation has the tendency to hinder bistable inversions, freeing it can even allow for extra stable configurations; however, a certain case is emphasised in which an increasing rotational spring stiffness causes a mode transition that stabilises inversions. In a second step, a polar-orthotropic material law is employed to study variations of the directional stiffness of the shell itself. A careful choice of the basis functions is required to accurately capture stress singularities in bending that arise if the radial Young’s modulus is stiffer than its circumferential equivalent. A simple way to circumvent such singularities is to create a central hole, which is shown not to hamper bistable inversions. For significantly stiffer values of the radial stiffness, a strong coupling with the support conditions is revealed: whilst roller-supported shells do not show a bistable inversion at all for such materials, fixed-pinned ones feel the most disposed to accommodate an alternative equilibrium configuration. This behaviour is explained via simplified beam models that suggest a new perspective on the influence of the hoop stiffness: based on observations in free-standing shells, it was thought to promote bistability, but it is only insofar stabilising, as it evokes radial stresses; if these are afforded by immovable supports, it becomes redundant and even slightly hindering. Finally, combined actuation methods in stretching and bending that prescribe non-Euclidean target shapes are considered to emphasise the possibility of multifarious structural manipulations. When both methods are geared to each other, stress-free synclastic shape transformations in an over-constrained environment, or alternatively, anticlastic shape-changes with an arbitrary wave number, are achievable. Considering nonsymmetric deformations offers a richer buckling behaviour for certain in-plane actuated shells, where a secondary, approximately cylindrical buckling mode as well as a ‘hidden’ stable configuration of a higher wave number is revealed by the presented analytical model. Additionally, it is shown that the approximately mirror-symmetric inversion of cylindrical or deep spherical shells can be accurately described by employing a simpler, geometrically linear theory that focusses on small deviations from the mirrored shape. The results of this dissertation facilitate a versatile practical application of multistable structures via an analytical description of more realistic support conditions. The understanding of effects of the internal stiffness makes it possible to use this unique structural behaviour more efficiently by making simple cross-sectional adjustments, i.e. by adding appropriate stiffeners. Eventually, the provided theoretical framework of emerging actuation methods might inspire novel morphing structures.Friedrich Ebert Foundation (Friedrich-Ebert-Stiftung) Corpus Christi College, Cambridge Department of Engineering, Cambridg

SPECIFIED MOTION AND FEEDBACK CONTROL OF ENGINEERING STRUCTURES WITH DISTRIBUTED SENSORS AND ACTUATORS

This dissertation addresses the control of flexible structures using distributed sensors and actuators. The objective to determine the required distributed actuation inputs such that the desired output is obtained. Two interrelated facets of this problem are considered. First, we develop a dynamic-inversion solution method for determining the distributed actuation inputs, as a function of time, that yield a specified motion. The solution is shown to be useful for intelligent structure design, in particular, for sizing actuators and choosing their placement. Secondly, we develop a new feedback control method, which is based on dynamic inversion. In particular, filtered dynamic inversion combines dynamic inversion with a low-pass filter, resulting in a high-parameter-stabilizing controller, where the parameter gain is the filter cutoff frequency. For sufficiently large parameter gain, the controller stabilizes the closed-loop system and makes the L2-gain of the performance arbitrarily small, despite unknown-and-unmeasured disturbances. The controller is considered for both linear and nonlinear structural models

Efficient computation of inverse dynamics and feedback linearization for VSA-based robots

We develop a recursive numerical algorithm to compute the inverse dynamics of robot manipulators with an arbitrary number of joints, driven by variable stiffness actuation (VSA) of the antagonistic type. The algorithm is based on Newton-Euler dynamic equations, generalized up to the fourth differential order to account for the compliant transmissions, combined with the decentralized nonlinear dynamics of the variable stiffness actuators at each joint. A variant of the algorithm can be used also for implementing a feedback linearization control law for the accurate tracking of desired link and stiffness trajectories. As in its simpler versions, the algorithm does not require dynamicmodeling in symbolic form, does not use numerical approximations, grows linearly in complexity with the number of joints, and is suitable for online feedforward and real-time feedback control. A Matlab/C code is made available

A Multistate Friction Model for the Compensation of the Asymmetric Hysteresis in the Mechanical Response of Pneumatic Artificial Muscles

These days, biomimetic and compliant actuators have been made available to the main applications of rehabilitation and assistive robotics. In this context, the interaction control of soft robots, mechatronic surgical instruments and robotic prostheses can be improved through the adoption of pneumatic artificial muscles (PAMs), a class of compliant actuators that exhibit some similarities with the structure and function of biological muscles. Together with the advantage of implementing adaptive compliance control laws, the nonlinear and hysteretic force/length characteristics of PAMs pose some challenges in the design and implementation of tracking control strategies. This paper presents a parsimonious and accurate model of the asymmetric hysteresis observed in the force response of PAMs. The model has been validated through the experimental identification of the mechanical response of a small-sized PAM where the asymmetric effects of hysteresis are more evident. Both the experimental results and a comparison with other dynamic friction models show that the proposed model could be useful to implement efficient compensation strategies for the tracking control of soft robots