Model-based Friction Compensation

Friction is present in all mechanical systems and causes a wide range of problems for control. The development of model-based strategies accounting for Friction in the designed control has been a vast area of Research since these last decades. A promising Friction model which received a lot of attention these last years is the so-called LuGre model, which originates in the collaboration between the two control Research groups of Lund (Sweden) and Grenoble (France). This model is quite simple and is capable of capturing a wide range of well known friction phenomena, such as the Stribeck effect or the frictionnal lag. In particular this model is used in [Robertsson et al., 2004], where a general method for friction compensation for nonlinear systems is presented. The compensation strategy is simple: it just consists in adding to the control signal a friction estimate, computed using a LuGre model based observer. This thesis deals with the application of the theory of this article on a real experiment: the stabilization of the Furuta pendulum in the upright position. First, attention is paid so that the initial hypothesis of this article be satisfied. These hypotheses consist in finding a stabilizing control for the system when Friction is neglected, and an associated Lyapunov function verifying some properties. Then, Friction is included by following the procedure presented in the article. The friction estimate is computed according to the discretized LuGre form, presented in fFreidovich et al., 2006g, and the main result of the article is verified both in Simulation and on the real process, the simulations being carried out with Matlab-Simulink and the real experiments by using a dSPACE device. From a practical point of view, the implemented compensation scheme works perfectly in Simulation: the limit cycles originating from an uncompensated friction are totally annihilated, while for real experiments this oscillating behaviour is still remaining, but happens to be significantly reduced. From a theoretical point of view, the results of [Robertsson et al., 2004] are fully verified in Simulation, while for real experiments the presence of remaining limit cycles prevents a perfect verification of the theory

Bio-inspired robotic control in underactuation: principles for energy efficacy, dynamic compliance interactions and adaptability.

Biological systems achieve energy efficient and adaptive behaviours through extensive autologous and exogenous compliant interactions. Active dynamic compliances are created and enhanced from musculoskeletal system (joint-space) to external environment (task-space) amongst the underactuated motions. Underactuated systems with viscoelastic property are similar to these biological systems, in that their self-organisation and overall tasks must be achieved by coordinating the subsystems and dynamically interacting with the environment. One important question to raise is: How can we design control systems to achieve efficient locomotion, while adapt to dynamic conditions as the living systems do? In this thesis, a trajectory planning algorithm is developed for underactuated microrobotic systems with bio-inspired self-propulsion and viscoelastic property to achieve synchronized motion in an energy efficient, adaptive and analysable manner. The geometry of the state space of the systems is explicitly utilized, such that a synchronization of the generalized coordinates is achieved in terms of geometric relations along the desired motion trajectory. As a result, the internal dynamics complexity is sufficiently reduced, the dynamic couplings are explicitly characterised, and then the underactuated dynamics are projected onto a hyper-manifold. Following such a reduction and characterization, we arrive at mappings of system compliance and integrable second-order dynamics with the passive degrees of freedom. As such, the issue of trajectory planning is converted into convenient nonlinear geometric analysis and optimal trajectory parameterization. Solutions of the reduced dynamics and the geometric relations can be obtained through an optimal motion trajectory generator. Theoretical background of the proposed approach is presented with rigorous analysis and developed in detail for a particular example. Experimental studies are conducted to verify the effectiveness of the proposed method. Towards compliance interactions with the environment, accurate modelling or prediction of nonlinear friction forces is a nontrivial whilst challenging task. Frictional instabilities are typically required to be eliminated or compensated through efficiently designed controllers. In this work, a prediction and analysis framework is designed for the self-propelled vibro-driven system, whose locomotion greatly relies on the dynamic interactions with the nonlinear frictions. This thesis proposes a combined physics-based and analytical-based approach, in a manner that non-reversible characteristic for static friction, presliding as well as pure sliding regimes are revealed, and the frictional limit boundaries are identified. Nonlinear dynamic analysis and simulation results demonstrate good captions of experimentally observed frictional characteristics, quenching of friction-induced vibrations and satisfaction of energy requirements. The thesis also performs elaborative studies on trajectory tracking. Control schemes are designed and extended for a class of underactuated systems with concrete considerations on uncertainties and disturbances. They include a collocated partial feedback control scheme, and an adaptive variable structure control scheme with an elaborately designed auxiliary control variable. Generically, adaptive control schemes using neural networks are designed to ensure trajectory tracking. Theoretical background of these methods is presented with rigorous analysis and developed in detail for particular examples. The schemes promote the utilization of linear filters in the control input to improve the system robustness. Asymptotic stability and convergence of time-varying reference trajectories for the system dynamics are shown by means of Lyapunov synthesis

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article

Prototyping Elliptically Profiled Inverted Pendulum Walls in Cross-laminated Timber (CLT) for Passive Self-centering and Seismic Resiliency

Cross-laminated timber (CLT) buildings garnered international attention, nearly a decade ago, for elevating wood construction to new heights on fully panelized assemblies of floors and walls. While highly regarded as a sustainable building material, use of CLT as a structural wall system depends on seismically resilient strategies like controlled rocking. This project prototyped elliptically profiled CLT panels and slotted-pin steel connections, at full-scale, to produce rolling and slip-friction inverted pendulum wall systems of one-story height and inspired by seismic isolation concepts. Digital fabrication realized elliptical profiles along the load-bearing edges of six 5-ply CLT panels and various customized slot shapes for accompanying steel connections. Pins traveling within V-shaped slots intended only to guide rolling as displacement restraints, in contrast with pins constrained within vertical slots that forced panels into slip-friction combinations of rolling and sliding. Six CLT panels and two versions of shear transfer connections yielded a total of 12 full-scale wall prototype configurations for cyclic lateral load-displacement testing that emulated standard quasi-static protocols for seismic isolation. The hysteresis plots generated by the tests confirmed that elliptical eccentricity predictably controlled effective lateral stiffness and displacement capacity, while providing inherent self-centering. When configured to roll using traction along steel bearing surfaces as the primary mechanism of story shear transfer, CLT panels supported simulated gravity loads as high as 400 kN (90 kips) while achieving story drifts commonly exceeding 10 and even 20 percent. When configured to transfer shear primarily through a pin connection, however, CLT panels slid and sustained damage that limited gravity load capacity to 133 kN (30 kips). Connection constraint, therefore, dictated whether friction essentially transferred story shears transfer or dissipated energy. To help explain implications of friction, Digital Image Correlation (DIC), piezoelectric film pressure mapping, Finite Element Analysis, and fundamental free-body diagrams visualized the behavior of high-pressure contact between timber and steel. Despite the low damping exhibited by rolling and increased damage of slip-friction rocking, both models of elliptically profiled rocking walls can develop into viable options for isolation planes within multistory building schemes, based on the results of this study

Climbing and Walking Robots

Nowadays robotics is one of the most dynamic fields of scientific researches. The shift of robotics researches from manufacturing to services applications is clear. During the last decades interest in studying climbing and walking robots has been increased. This increasing interest has been in many areas that most important ones of them are: mechanics, electronics, medical engineering, cybernetics, controls, and computers. Today’s climbing and walking robots are a combination of manipulative, perceptive, communicative, and cognitive abilities and they are capable of performing many tasks in industrial and non- industrial environments. Surveillance, planetary exploration, emergence rescue operations, reconnaissance, petrochemical applications, construction, entertainment, personal services, intervention in severe environments, transportation, medical and etc are some applications from a very diverse application fields of climbing and walking robots. By great progress in this area of robotics it is anticipated that next generation climbing and walking robots will enhance lives and will change the way the human works, thinks and makes decisions. This book presents the state of the art achievments, recent developments, applications and future challenges of climbing and walking robots. These are presented in 24 chapters by authors throughtot the world The book serves as a reference especially for the researchers who are interested in mobile robots. It also is useful for industrial engineers and graduate students in advanced study

Friction compensation in the swing-up control of viscously damped underactuated robotics

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering in the Control Research Group School of Electrical and Information Engineering, Johannesburg, 2017In this research, we observed a torque-related limitation in the swing-up control of underactuated mechanical systems which had been integrated with viscous damping in the unactuated joint. The objective of this research project was thus to develop a practical work-around solution to this limitation. The nth order underactuated robotic system is represented in this research as a collection of compounded pendulums with n-1 actuators placed at each joint with the exception of the first joint. This system is referred to as the PAn-1 robot (Passive first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA robot (or PA2 robot) being among the most well-known examples. A number of friction models exist in literature, which include, and are not exclusive to, the Coulomb and the Stribeck effect models, but the viscous damping model was selected for this research since it is more extensively covered in existing literature. The effectiveness of swing-up control using Lyapunov’s direct method when applied on the undamped PAn-1 robot has been vigorously demonstrated in existing literature, but there is no literature that discusses the swing-up control of viscously damped systems. We show, however, that the application of satisfactory swing-up control using Lyapunov’s direct method is constrained to underactuated systems that are either undamped or actively damped (viscous damping integrated into the actuated joints only). The violation of this constraint results in the derivation of a torque expression that cannot be solved for (invertibility problem, for systems described by n > 2) or a torque expression which contains a conditional singularity (singularity problem, for systems with n = 2). This constraint is formally summarised as the matched damping condition, and highlights a clear limitation in the Lyapunov-related swing-up control of underactuated mechanical systems. This condition has significant implications on the practical realisation of the swing-up control of underactuated mechanical systems, which justifies the investigation into the possibility of a work-around. We thus show that the limitation highlighted by the matched damping condition can be overcome through the implementation of the partial feedback linearisation (PFL) technique. Two key contributions are generated from this research as a result, which iii include the gain selection criterion (for Traditional Collocated PFL), and the convergence algorithm (for noncollocated PFL). The gain selection criterion is an analytical solution that is composed of a set of inequalities that map out a geometric region of appropriate gains in the swing-up gain space. Selecting a gain combination within this region will ensure that the fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition for swing-up control when the system is initialised near the FPEP. The convergence algorithm is an experimental solution that, once executed, will provide information about the distal pendulum’s angular initial condition that is required to swing-up a robot with a particular angular initial condition for the proximal pendulum, along with the minimum gain that is required to execute the swing-up control in this particular configuration. Significant future contributions on this topic may result from the inclusion of more complex friction models. Additionally, the degree of actuation of the system may be reduced through the implementation of energy storing components, such as torsional springs, at the joint. In summary, we present two contributions in the form of the gain selection criterion and the convergence algorithm which accommodate the circumnavigation of the limitation formalised as the matched damping condition. This condition pertains to the Lyapunov-related swing-up control of underactuated mechanical systems that have been integrated with viscous damping in the unactuated joint.CK201