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

Passive dynamic walking with knees : a point foot model

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 57-59).In this thesis, a hybrid model for a passive 2D walker with knees and point feet is presented. The step cycle of the model has two phases of continuous dynamics: one with an unlocked knee configuration and a second one with a locked knee configuration. These stages are modeled as three-link and two-link pendulums correspondingly. The model switches between the two stages at knee-strike and heel-strike, which are both discrete events modeled as instantaneous inelastic collisions. The dynamics of this model were fully derived analytically. Furthermore, a stable gait was found given a set of physical parameters and initial conditions. A basic stability analysis of this stable limit cycle was performed around the fixed point of the Poincar6 return map examined right after heel-strike. This thesis also presents the design and construction of a planar robot based on this kneed walker model, as well as a careful examination of its correspondence to the motion predicted by the model simulation. The goal is to be able to study the nonlinear dynamics of simplified dynamic models which are also physically realizable, in order to build robots based on them in a more rigorous and reproducible manner. The work presented here aims to bridge the gap between existing theoretical models and successful experiments in passive dynamic walking.by Vanessa F. Hsu Chen.M.Eng

The design and control of an actively restrained passive mechatronic system for safety-critical applications

Development of manipulators that interact closely with humans has been a focus of research in fields such as robot-assisted surgery and haptic interfaces for many years. Recent introduction of powered surgical-assistant devices into the operating theatre has meant that robot manipulators have been required to interact with both patients and surgeons. Most of these manipulators are modified industrial robots. However, the use of high-powered mechanisms in the operating theatre could compromise safety of the patient, surgeon, and operating room staff. As a solution to the safety problem, the use of actively restrained passive arms has been proposed. Clutches or brakes at each joint are used to restrict the motion of the end-effector to restrain it to a pre-defined region or path. However, these devices have only had limited success in following pre-defined paths under human guidance. In this research, three major limitations of existing passive devices actively restrained are addressed. [Continues.

Design, modelling and control of a brachiating power line inspection robot

The inspection of power lines and associated hardware is vital to ensuring the reliability of the transmission and distribution network. The repetitive nature of the inspection tasks present a unique opportunity for the introduction of robotic platforms, which offer the ability to perform more systematic and detailed inspection than traditional methods. This lends itself to improved asset management automation, cost-effectiveness and safety for the operating crew. This dissertation presents the development of a prototype industrial brachiating robot. The robot is mechanically simple and capable of dynamically negotiating obstacles by brachiating. This is an improvement over current robotic platforms, which employ slow, high power static schemes for obstacle negotiation. Mathematical models of the robot were derived to understand the underlying dynamics of the system. These models were then used in the generation of optimal trajectories, using nonlinear optimisation techniques, for brachiating past line hardware. A physical robot was designed and manufactured to validate the brachiation manoeuvre. The robot was designed following classic mechanical design principles, with emphasis on functional design and robustness. System identification was used to capture the plant uncertainty and a feedback controller was designed to track the reference trajectory allowing for energy optimal brachiation swings. Finally, the robot was tested, starting with sub-system testing and ending with testing of a brachiation manoeuvre proving the prospective viability of the robot in an industrial environment

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Trajectory Exploration and Maneuver Regulation of the Pendubot

The pendulum provides a seemingly inexhaustible source of practical applications and interesting problems which have motivated research in a variety of disciplines. In this thesis, we study equations that described a driven pendulum with odd-periodic driving. The equations also describe the under-actuated, double pendulum system called the pendubot. Techniques for trajectory exploration are developed. For the inverted pendulum, we first wrote the problem as a two point boundary value problem with Dirichlet boundary conditions. Then, we develop an equivalent linear operator that combines a Nemitski operator (or superposition operator) with the linear operator for the unstable harmonic oscillator. By exploring the properties of the Green’s function for the unstable harmonic oscillator with Dirichlet boundary conditions, we developed bounds on various norms that prove useful for determining which parameter values will satisfy invariance and contraction conditions. With a direct application of the Schauder fixed point theorem, we showed that our family of equations representing an inverted pendulum always possessed an odd-periodic solution. Using the Banach fixed point theorem we showed that there is a unique solution within an invariant region of the space of possible solution curves. When there is a unique solution, successive approximations can be used to compute the solution trajectory. To illustrate the power and application of these ideas, we apply them to a pendubot with the inner arm moving at a constant velocity. For non-inverted trajectories of the pendubot, we presented a necessary condition for trajectories to exist with general periodic forcing. For odd-periodic periodic driving functions this condition is always satisfied. For a driving function of A sin(wt), we found multiple solutions for the outer link. With the trajectories in hand, we demonstrated through simulation and/or physical implementation, the usefulness of maneuver regulation for providing orbital stabilization

Cable-driven parallel mechanisms for minimally invasive robotic surgery

Minimally invasive surgery (MIS) has revolutionised surgery by providing faster recovery times, less post-operative complications, improved cosmesis and reduced pain for the patient. Surgical robotics are used to further decrease the invasiveness of procedures, by using yet smaller and fewer incisions or using natural orifices as entry point. However, many robotic systems still suffer from technical challenges such as sufficient instrument dexterity and payloads, leading to limited adoption in clinical practice. Cable-driven parallel mechanisms (CDPMs) have unique properties, which can be used to overcome existing challenges in surgical robotics. These beneficial properties include high end-effector payloads, efficient force transmission and a large configurable instrument workspace. However, the use of CDPMs in MIS is largely unexplored. This research presents the first structured exploration of CDPMs for MIS and demonstrates the potential of this type of mechanism through the development of multiple prototypes: the ESD CYCLOPS, CDAQS, SIMPLE, neuroCYCLOPS and microCYCLOPS. One key challenge for MIS is the access method used to introduce CDPMs into the body. Three different access methods are presented by the prototypes. By focusing on the minimally invasive access method in which CDPMs are introduced into the body, the thesis provides a framework, which can be used by researchers, engineers and clinicians to identify future opportunities of CDPMs in MIS. Additionally, through user studies and pre-clinical studies, these prototypes demonstrate that this type of mechanism has several key advantages for surgical applications in which haptic feedback, safe automation or a high payload are required. These advantages, combined with the different access methods, demonstrate that CDPMs can have a key role in the advancement of MIS technology.Open Acces

Robust and Economical Bipedal Locomotion

For bipedal robots to gain widespread use, significant improvements must be made in their energetic economy and robustness against falling. An increase in economy can increase their functional range, while a reduction in the rate of falling can reduce the need for human intervention. This dissertation explores novel concepts that improve these two goals in a fundamental manner. By centering on core ideas instead of direct application, these concepts are aimed at influencing a wide range of current and future legged robots. The presented work can be broken into five major contributions. The first extends our understanding of the energetic economy of series elastic walking robots. This investigation uses trajectory optimization to find energy-miminizing periodic motions for a realistic model of the walking robot RAMone. The energetically optimal motions for this model are shown to closely resemble human walking at low speeds, and as the speed increases, the motions switch abruptly to those resembling human running. The second contribution explores the energetic economy of the real robot RAMone. Here the model used in the previous investigation is shown to closely match reality. In addition, this investigation demonstrates a concrete example of a trade-off between energetic economy and robustness. The third contribution takes a step towards addressing this trade-off by deriving a robot constraint that guarantees safety against falling. Such a constraint can be used to remove considerations of robustness while conducting future investigations into economical robot motions. The approach is demonstrated using a simple compass-gait style walking model. The fourth contribution extends this safety constraint towards higher-dimensional walking models, using a combination of hybrid zero dynamics and sums-of-squares analysis. This is demonstrated by safely modifying the pitch of a 10 dimensional Rabbit model walking over flat terrain. The final contribution pushes the safety guarantee towards a broader set of walking behaviours, including rough terrain walking. Throughout this work, a range of models are used to reason about the economy and robustness of walking robots. These model-based methods allow control designers to move away from heuristics and tuning, and towards generalizable and reliable controllers. This is vital for walking robots to push further into the wild.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153459/1/nilssmit_1.pd