Advances in PID Control

Since the foundation and up to the current state-of-the-art in control engineering, the problems of PID control steadily attract great attention of numerous researchers and remain inexhaustible source of new ideas for process of control system design and industrial applications. PID control effectiveness is usually caused by the nature of dynamical processes, conditioned that the majority of the industrial dynamical processes are well described by simple dynamic model of the first or second order. The efficacy of PID controllers vastly falls in case of complicated dynamics, nonlinearities, and varying parameters of the plant. This gives a pulse to further researches in the field of PID control. Consequently, the problems of advanced PID control system design methodologies, rules of adaptive PID control, self-tuning procedures, and particularly robustness and transient performance for nonlinear systems, still remain as the areas of the lively interests for many scientists and researchers at the present time. The recent research results presented in this book provide new ideas for improved performance of PID control applications

Passivity-Based adaptive bilateral teleoperation control for uncertain manipulators without jerk measurements

In this work, we consider the bilateral teleoperation problem of cooperative robotic systems in a Single-Master Multi-Slave (SM/MS) configuration, which is able to perform load transportation tasks in the presence of parametric uncertainty in the robot kinematic and dynamic models. The teleoperation architecture is based on the two-layer approach placed in a hierarchical structure, whose top and bottom layers are responsible for ensuring the transparency and stability properties respectively. The load transportation problem is tackled by using the formation control approach wherein the desired translational velocity and interaction force are provided to the master robot by the user, while the object is manipulated with a bounded constant force by the slave robots. Firstly, we develop an adaptive kinematic-based control scheme based on a composite adaptation law to solve the cooperative control problem for robots with uncertain kinematics. Secondly, the dynamic adaptive control for cooperative robots is implemented by means of a cascade control strategy, which does not require the measurement of the time derivative of force (which requires jerk measurements). The combination of the Lyapunov stability theory and the passivity formalism are used to establish the stability and convergence property of the closed-loop control system. Simulations and experimental results illustrate the performance and feasibility of the proposed control scheme.No presente trabalho, considera-se o problema de teleoperação bilateral de um sistema robótico cooperativo do tipo single-master e multiple-slaves (SM/MS) capaz de realizar tarefas de transporte de carga na presença de incertezas paramétricas no modelo cinemático e dinâmico dos robôs. A arquitetura de teleoperação está baseada na abordagem de duas camadas em estrutura hierárquica, onde as camadas superior e inferior são responsáveis por assegurar as propriedades de transparência e estabilidade respectivamente. O problema de transporte de carga é formulado usando a abordagem de controle de formação onde a velocidade de translação desejada e a força de interação são fornecidas ao robô mestre pelo operador, enquanto o objeto é manipulado pelos robôs escravos com uma força constante limitada. Primeiramente, desenvolve-se um esquema de controle adaptativo cinemático baseado em uma lei de adaptação composta para solucionar o problema de controle cooperativo de robôs com cinemática incerta. Em seguida, o controle adaptativo dinâmico de robôs cooperativos é implementado por meio de uma estratégia de controle em cascata, que não requer a medição da derivada da força (o qual requer a derivada da aceleração ou jerk). A teoria de estabilidade de Lyapunov e o formalismo de passividade são usados para estabelecer as propriedades de estabilidade e a convergência do sistema de controle em malha-fechada. Resultados de simulações numéricas ilustram o desempenho e viabilidade da estratégia de controle proposta

Adaptive control of compliant robots with Reservoir Computing

In modern society, robots are increasingly used to handle dangerous, repetitive and/or heavy tasks with high precision. Because of the nature of the tasks, either being dangerous, high precision or simply repetitive, robots are usually constructed with high torque motors and sturdy materials, that makes them dangerous for humans to handle. In a car-manufacturing company, for example, a large cage is placed around the robot’s workspace that prevents humans from entering its vicinity. In the last few decades, efforts have been made to improve human-robot interaction. Often the movement of robots is characterized as not being smooth and clearly dividable into sub-movements. This makes their movement rather unpredictable for humans. So, there exists an opportunity to improve the motion generation of robots to enhance human-robot interaction. One interesting research direction is that of imitation learning. Here, human motions are recorded and demonstrated to the robot. Although the robot is able to reproduce such movements, it cannot be generalized to other situations. Therefore, a dynamical system approach is proposed where the recorded motions are embedded into the dynamics of the system. Shaping these nonlinear dynamics, according to recorded motions, allows for dynamical system to generalize beyond demonstration. As a result, the robot can generate motions of other situations not included in the recorded human demonstrations. In this dissertation, a Reservoir Computing approach is used to create a dynamical system in which such demonstrations are embedded. Reservoir Computing systems are Recurrent Neural Network-based approaches that are efficiently trained by considering only the training of the readout connections and retaining all other connections of such a network unchanged given their initial randomly chosen values. Although they have been used to embed periodic motions before, they were extended to embed discrete motions, or both. This work describes how such a motion pattern-generating system is built, investigates the nature of the underlying dynamics and evaluates their robustness in the face of perturbations. Additionally, a dynamical system approach to obstacle avoidance is proposed that is based on vector fields in the presence of repellers. This technique can be used to extend the motion abilities of the robot without need for changing the trained Motion Pattern Generator (MPG). Therefore, this approach can be applied in real-time on any system that generates a certain movement trajectory. Assume that the MPG system is implemented on an industrial robotic arm, similar to the ones used in a car factory. Even though the obstacle avoidance strategy presented is able to modify the generated motion of the robot’s gripper in such a way that it avoids obstacles, it does not guarantee that other parts of the robot cannot collide with a human. To prevent this, engineers have started to use advanced control algorithms that measure the amount of torque that is applied on the robot. This allows the robot to be aware of external perturbations. However, it turns out that, even with fast control loops, the adaptation to compensate for a sudden perturbation, is too slow to prevent high interaction forces. To reduce such forces, researchers started to use mechanical elements that are passively compliant (e.g., springs) and light-weight flexible materials to construct robots. Although such compliant robots are much safer and inherently energy efficient to use, their control becomes much harder. Most control approaches use model information about the robot (e.g., weight distribution and shape). However, when constructing a compliant robot it is hard to determine the dynamics of these materials. Therefore, a model-free adaptive control framework is proposed that assumes no prior knowledge about the robot. By interacting with the robot it learns an inverse robot model that is used as controller. The more it interacts, the better the control be- comes. Appropriately, this framework is called Inverse Modeling Adaptive (IMA) control framework. I have evaluated the IMA controller’s tracking ability on sev- eral tasks, investigating its model independence and stability. Furthermore, I have shown its fast learning ability and comparable performance to taskspecific designed controllers. Given both the MPG and IMA controllers, it is possible to improve the inter- actability of a compliant robot in a human-friendly environment. When the robot is to perform human-like motions for a large set of tasks, we need to demonstrate motion examples of all these tasks. However, biological research concerning the motion generation of animals and humans revealed that a limited set of motion patterns, called motion primitives, are modulated and combined to generate advanced motor/motion skills that humans and animals exhibit. Inspired by these interesting findings, I investigate if a single motion primitive indeed can be modulated to achieve a desired motion behavior. By some elementary experiments, where an MPG is controlled by an IMA controller, a proof of concept is presented. Furthermore, a general hierarchy is introduced that describes how a robot can be controlled in a biology-inspired manner. I also investigated how motion primitives can be combined to produce a desired motion. However, I was unable to get more advanced implementations to work. The results of some simple experiments are presented in the appendix. Another approach I investigated assumes that the primitives themselves are undefined. Instead, only a high-level description is given, which describes that every primitive on average should contribute equally, while still allowing for a single primitive to specialize in a part of the motion generation. Without defining the behavior of a primitive, only a set of untrained IMA controllers is used of which each will represent a single primitive. As a result of the high-level heuristic description, the task space is tiled into sub-regions in an unsupervised manner. Resulting in controllers that indeed represent a part of the motion generation. I have applied this Modular Architecture with Control Primitives (MACOP) on an inverse kinematic learning task and investigated the emerged primitives. Thanks to the tiling of the task space, it becomes possible to control redundant systems, because redundant solutions can be spread over several control primitives. Within each sub region of the task space, a specific control primitive is more accurate than in other regions allowing for the task complexity to be distributed over several less complex tasks. Finally, I extend the use of an IMA-controller, which is tracking controller, to the control of under-actuated systems. By using a sample-based planning algorithm it becomes possible to explore the system dynamics in which a path to a desired state can be planned. Afterwards, MACOP is used to incorporate feedback and to learn the necessary control commands corresponding to the planned state space trajectory, even if it contains errors. As a result, the under-actuated control of a cart pole system was achieved. Furthermore, I presented the concept of a simulation based control framework that allows the learning of the system dynamics, planning and feedback control iteratively and simultaneously

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

From Underactuation to Quasi‐Full Actuation: A Unifying Control Framework for Rigid and Elastic Joint Robot

The quest for animal-like performance in robots has driven the integration of elastic elements in their drive trains, sparking a revolution in robot design. Elastic robots can store and release potential energy, providing distinct advantages over traditional robots, such as enhanced safety in human-robot interaction, resilience to mechanical shocks, improved energy efficiency in cyclic tasks, and dynamic motion capabilities. Exploiting their full potential, however, necessitates novel control methods. This thesis advances the field of nonlinear control for underactuated systems and utilizes the results to push the boundaries of motion and interaction performance of elastic robots. Through real-life experiments and applications, the proposed controllers demonstrate that compliant robots hold promise as groundbreaking robotic technology. To achieve these objectives, we first derive a simultaneous phase space and input transformation that enables a specific class of underactuated Lagrangian systems to be treated as if fully actuated. These systems can be represented as the interconnection of actuated and underactuated subsystems, with the kinetic energy of each subsystem depending only on its own velocity. Elastic robots are typical representatives. We refer to the transformed system as quasi-fully actuated due to weak constraints on the new inputs. Fundamental aspects of the transforming equations are 1) the same Lagrangian function characterizes both the original and transformed systems, 2) the transformed system establishes a passive mapping between inputs and outputs, and 3) the solutions of both systems are in a one-to-one correspondence, describing the same physical reality. This correspondence allows us to study and control the behavior of the quasi-fully actuated system instead of the underactuated one. Thus, this approach unifies the control design for rigid and elastic joint robots, enabling the direct application of control results inherited from the fully-actuated case while ensuring closed-loop system stability and passivity. Unlike existing methods, the quasi-full actuation concept does not rely on inner control loops or the neglect and cancellation of dynamics. Notably, as joint stiffness values approach infinity, the control equivalent of a rigid robot is recovered. Building upon the quasi-full actuation concept, we extend energy-based control schemes such as energy shaping and damping injection, Euler-Lagrange controllers, and impedance control. Moreover, we introduce Elastic Structure Preserving (ESP) control, a passivity-based control scheme designed for robots with elastic or viscoelastic joints, guided by the principle of ``do as little as possible''. The underlying hope is that reducing the system shaping, i.e., having a closed-loop dynamics match in some way the robot's intrinsic structure, will award high performance with little control effort. By minimizing the system shaping, we obtain low-gain designs, which are favorable concerning robustness and facilitate the emergence of natural motions. A comparison with state-of-the-art controllers highlights the minimalistic nature of ESP control. Additionally, we present a synthesis method, based on purely geometric arguments, for achieving time-optimal rest-to-rest motions of an elastic joint with bounded input. Finally, we showcase the remarkable performance and robustness of the proposed ESP controllers on DLR David, an anthropomorphic robot implemented with variable impedance actuators. Experimental evidence reveals that ESP designs enable safe and compliant interaction with the environment and rigid-robot-level accuracy in free motion. Additionally, we introduce a control framework that allows DLR David to perform commercially relevant tasks, such as pick and place, teleoperation, hammer drilling into a concrete block, and unloading a dishwasher. The successful execution of these tasks provides compelling evidence that compliant robots have a promising future in commercial applications

Energy Shaping of Mechanical Systems via Control Lyapunov Functions with Applications to Bipedal Locomotion

This dissertation presents a method which attempts to improve the stability properties of periodic orbits in hybrid dynamical systems by shaping the energy. By taking advantage of conservation of energy and the existence of invariant level sets of a conserved quantity of energy corresponding to periodic orbits, energy shaping drives a system to a desired level set. This energy shaping method is similar to existing methods but improves upon them by utilizing control Lyapunov functions, allowing for formal results on stability. The main theoretical result, Theorem 1, states that, given an exponentially-stable limit cycle in a hybrid dynamical system, application of the presented energy shaping controller results in a closed-loop system which is exponentially stable. The method can be applied to a wide class of problems including bipedal locomotion; because the optimization problem can be formulated as a quadratic program operating on a convex set, existing methods can be used to rapidly obtain the optimal solution. As illustrated through numerical simulations, this method turns out to be useful in practice, taking an existing behavior which corresponds to a periodic orbit of a hybrid system, such as steady state locomotion, and providing an improvement in convergence properties and robustness with respect to perturbations in initial conditions without destabilizing the behavior. The method is even shown to work on complex multi-domain hybrid systems; an example is provided of bipedal locomotion for a robot with non-trivial foot contact which results in a multi-phase gait

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

Safe Haptics-enabled Patient-Robot Interaction for Robotic and Telerobotic Rehabilitation of Neuromuscular Disorders: Control Design and Analysis

Motivation: Current statistics show that the population of seniors and the incidence rate of age-related neuromuscular disorders are rapidly increasing worldwide. Improving medical care is likely to increase the survival rate but will result in even more patients in need of Assistive, Rehabilitation and Assessment (ARA) services for extended periods which will place a significant burden on the world\u27s healthcare systems. In many cases, the only alternative is limited and often delayed outpatient therapy. The situation will be worse for patients in remote areas. One potential solution is to develop technologies that provide efficient and safe means of in-hospital and in-home kinesthetic rehabilitation. In this regard, Haptics-enabled Interactive Robotic Neurorehabilitation (HIRN) systems have been developed. Existing Challenges: Although there are specific advantages with the use of HIRN technologies, there still exist several technical and control challenges, e.g., (a) absence of direct interactive physical interaction between therapists and patients; (b) questionable adaptability and flexibility considering the sensorimotor needs of patients; (c) limited accessibility in remote areas; and (d) guaranteeing patient-robot interaction safety while maximizing system transparency, especially when high control effort is needed for severely disabled patients, when the robot is to be used in a patient\u27s home or when the patient experiences involuntary movements. These challenges have provided the motivation for this research. Research Statement: In this project, a novel haptics-enabled telerobotic rehabilitation framework is designed, analyzed and implemented that can be used as a new paradigm for delivering motor therapy which gives therapists direct kinesthetic supervision over the robotic rehabilitation procedure. The system also allows for kinesthetic remote and ultimately in-home rehabilitation. To guarantee interaction safety while maximizing the performance of the system, a new framework for designing stabilizing controllers is developed initially based on small-gain theory and then completed using strong passivity theory. The proposed control framework takes into account knowledge about the variable biomechanical capabilities of the patient\u27s limb(s) in absorbing interaction forces and mechanical energy. The technique is generalized for use for classical rehabilitation robotic systems to realize patient-robot interaction safety while enhancing performance. In the next step, the proposed telerobotic system is studied as a modality of training for classical HIRN systems. The goal is to first model and then regenerate the prescribed kinesthetic supervision of an expert therapist. To broaden the population of patients who can use the technology and HIRN systems, a new control strategy is designed for patients experiencing involuntary movements. As the last step, the outcomes of the proposed theoretical and technological developments are translated to designing assistive mechatronic tools for patients with force and motion control deficits. This study shows that proper augmentation of haptic inputs can not only enhance the transparency and safety of robotic and telerobotic rehabilitation systems, but it can also assist patients with force and motion control deficiencies

System Identification of Bipedal Locomotion in Robots and Humans

The ability to perform a healthy walking gait can be altered in numerous cases due to gait disorder related pathologies. The latter could lead to partial or complete mobility loss, which affects the patients’ quality of life. Wearable exoskeletons and active prosthetics have been considered as a key component to remedy this mobility loss. The control of such devices knows numerous challenges that are yet to be addressed. As opposed to fixed trajectories control, real-time adaptive reference generation control is likely to provide the wearer with more intent control over the powered device. We propose a novel gait pattern generator for the control of such devices, taking advantage of the inter-joint coordination in the human gait. Our proposed method puts the user in the control loop as it maps the motion of healthy limbs to that of the affected one. To design such control strategy, it is critical to understand the dynamics behind bipedal walking. We begin by studying the simple compass gait walker. We examine the well-known Virtual Constraints method of controlling bipedal robots in the image of the compass gait. In addition, we provide both the mechanical and control design of an affordable research platform for bipedal dynamic walking. We then extend the concept of virtual constraints to human locomotion, where we investigate the accuracy of predicting lower limb joints angular position and velocity from the motion of the other limbs. Data from nine healthy subjects performing specific locomotion tasks were collected and are made available online. A successful prediction of the hip, knee, and ankle joints was achieved in different scenarios. It was also found that the motion of the cane alone has sufficient information to help predict good trajectories for the lower limb in stairs ascent. Better estimates were obtained using additional information from arm joints. We also explored the prediction of knee and ankle trajectories from the motion of the hip joints

Control Implementation of Dynamic Locomotion on Compliant, Underactuated, Force-Controlled Legged Robots with Non-Anthropomorphic Design

The control of locomotion on legged robots traditionally involves a robot that takes a standard legged form, such as the anthropomorphic humanoid, the dog-like quadruped, or the bird-like biped. Additionally, these systems will often be actuated with position-controlled servos or series-elastic actuators that are connected through rigid links. This work investigates the control implementation of dynamic, force-controlled locomotion on a family of legged systems that significantly deviate from these classic paradigms by incorporating modern, state-of-the-art proprioceptive actuators on uniquely configured compliant legs that do not closely resemble those found in nature. The results of this work can be used to better inform how to implement controllers on legged systems without stiff, position-controlled actuators, and also provide insight on how intelligently designed mechanical features can potentially simplify the control of complex, nonlinear dynamical systems like legged robots. To this end, this work presents the approach to control for a family of non-anthropomorphic bipedal robotic systems which are developed both in simulation and with physical hardware. The first is the Non-Anthropomorphic Biped, Version 1 (NABi-1) that features position-controlled joints along with a compliant foot element on a minimally actuated leg, and is controlled using simple open-loop trajectories based on the Zero Moment Point. The second system is the second version of the non-anthropomorphic biped (NABi-2) which utilizes the proprioceptive Back-drivable Electromagnetic Actuator for Robotics (BEAR) modules for actuation and fully realizes feedback-based force controlled locomotion. These systems are used to highlight both the strengths and weaknesses of utilizing proprioceptive actuation in systems, and suggest the tradeoffs that are made when using force control for dynamic locomotion. These systems also present case studies for different approaches to system design when it comes to bipedal legged robots