A virtual holonomic constraint (VHC) for an Euler-Lagrange Control System is a smooth relation between the configuration variables that can be made invariant through application of suitable feedback. In this thesis we investigate the role played by VHCs in the synchronization of Euler-Lagrange systems. We focus on two problems. For $N$ underactuated cart-pendulums, we design a smooth feedback that fully synchronizes the cart-pendulums while simultaneously stabilizing a periodic orbit corresponding to a desired oscillation for the pendulums. A by-product of our results is the ability to simultaneously synchronize the pendulums and stabilize the unstable upright equilibrium. The second synchronization problem investigated in this thesis is bilateral teleoperation, whereby a master robot is operated by a human while a slave robot synchronizes to the master. For two identical planar manipulators, we develop a methodology to achieve teleoperation in the presence of a hard surface, with simultaneous force control.

A virtual holonomic constraint (VHC) for an Euler-Lagrange Control System is a smooth relation between the configuration variables that can be made invariant through application of suitable feedback. In this thesis we investigate the role played by VHCs in the synchronization of Euler-Lagrange systems. We focus on two problems. For $N$ underactuated cart-pendulums, we design a smooth feedback that fully synchronizes the cart-pendulums while simultaneously stabilizing a periodic orbit corresponding to a desired oscillation for the pendulums. A by-product of our results is the ability to simultaneously synchronize the pendulums and stabilize the unstable upright equilibrium. The second synchronization problem investigated in this thesis is bilateral teleoperation, whereby a master robot is operated by a human while a slave robot synchronizes to the master. For two identical planar manipulators, we develop a methodology to achieve teleoperation in the presence of a hard surface, with simultaneous force control.

Forestry machines have the power to lift heavy logs, but they are not so smart at providing information, or help operators perform better work. The main reason to this problem is the low level of technology applied to forestry machines, which has not changed so much since the forestry machines were first introduced in the 1960’s. But starting 2013, machines manufacturers got inspired by developments in the automation and robotics industry, several of new technologies have been developed in the market - computerized hydraulics, feedback controllers for vibration damping, sensor-based motion control systems, improvements in mechanical design, smart suspension controller, etc. Largely, this development is attributed to better hardware and software developed during the last decade by researchers of Scandinavian institutes. In this thesis, we introduce a new type of forestry machine, the harwarder, which can perform the work of two machines (harvester and forwarder) by a single one. The forwarder is a forestry vehicle that carries big felled logs. The harvester is a type of heavy forestry manipulator employed in cut-to-length logging operations for felling, and bucking trees. Both the manipulator and vehicle should work synchronized to get the best out of this design. To benefit out of its design, in the first part of thesis we will analyze the kinematics and dynamics of machine, and design a time optimal coordinated motion via virtual holonomic constraints, to solve a particular task of forestry crane. The second part consists on applying optimization to reduce energy consumption during the motion. Result of thesis work: 1) By using coordinated motion, consequently the energy consumptions are drastically reduced comparing to traditional motion of the crane. 2) By applying optimization, the energy efficiency is improved.

<p>In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. One can think of human-like machines that may replace humans in hazardous working areas, perform enduring assembly tasks, serve the elderly and handicapped, etc. The main challenges in the development of such robots are, first, to construct sophisticated electro-mechanical humanoids and, second, to plan and control human-like motor patterns.</p><p>A promising idea for motion planning and control is to reparameterize any somewhat coordinated motion in terms of virtual holonomic constraints, i.e. trajectories of all degrees of freedom of the mechanical system are described by geometric relations among the generalized coordinates. Imposing such virtual holonomic constraints on the system dynamics allows to generate synchronized motor patterns by feedback control. In fact, there exist consistent geometric relations in ordinary human movements that can be used advantageously. In this thesis the virtual constraints approach is extended to a wider and rigorous use for analyzing, planning and reproducing human-like motions based on mathematical tools previously utilized for very particular control problems.</p><p>It is often the case that some desired motions cannot be achieved by the robot due to limitations in available actuation power. This constraint rises the question of how to modify the mechanical design in order to achieve better performance. An underactuated planar two-link robot is used to demonstrate that springs can complement the actuation in parallel to an ordinary motor. Motion planning is carried out for the original robot dynamics while the springs are treated as part of the control action with a torque profile suited to the preplanned trajectory.</p><p>Another issue discussed in this thesis is to find stable and unstable (hybrid) limit cycles for passive dynamic walking robots without integrating the full set of differential equations. Such procedure is demonstrated for the compass-gait biped by means of optimization with a reduced number of initial conditions and parameters to search. The properties of virtual constraints and reduced dynamics are exploited to solve this problem.</p>

Whether it is a car, a mobile phone, or a computer, we are noticing how automation and production with robots plays an important role in the industry of our modern world. We find it in factories, manufacturing products, automotive cruise control, construction equipment, autopilot on airplanes, and countless other industrial applications.         Automation technology can vary greatly depending on the field of application. On one end, we have systems that are operated by the user and rely fully on human ability. Examples of these are heavy-mobile equipment, remote controlled systems, helicopters, and many more. On the other end, we have autonomous systems that are able to make algorithmic decisions independently of the user.         Society has always envisioned robots with the full capabilities of humans. However, we should envision applications that will help us increase productivity and improve our quality of life through human-robot collaboration. The questions we should be asking are: “What tasks should be automated?'', and “How can we combine the best of both humans and automation?”. This thinking leads to the idea of developing systems with some level of autonomy, where the intelligence is shared between the user and the system. Reasonably, the computerized intelligence and decision making would be designed according to mathematical algorithms and control rules.         This thesis considers these topics and shows the importance of fundamental mathematics and control design to develop automated systems that can execute desired tasks. All of this work is based on some of the most modern concepts in the subjects of robotics and control, which are synthesized by a method known as the Virtual Holonomic Constraints Approach. This method has been useful to tackle some of the most complex problems of nonlinear control, and has enabled the possibility to approach challenging academic and industrial problems. This thesis shows concepts of system modeling, control design, motion analysis, motion planning, and many other interesting subjects, which can be treated effectively through analytical methods. The use of mathematical approaches allows performing computer simulations that also lead to direct practical implementations.

In the field of robotics there is a great interest in developing strategies and algorithms to reproduce human-like behavior. One can think of human-like machines that may replace humans in hazardous working areas, perform enduring assembly tasks, serve the elderly and handicapped, etc. The main challenges in the development of such robots are, first, to construct sophisticated electro-mechanical humanoids and, second, to plan and control human-like motor patterns. A promising idea for motion planning and control is to reparameterize any somewhat coordinated motion in terms of virtual holonomic constraints, i.e. trajectories of all degrees of freedom of the mechanical system are described by geometric relations among the generalized coordinates. Imposing such virtual holonomic constraints on the system dynamics allows to generate synchronized motor patterns by feedback control. In fact, there exist consistent geometric relations in ordinary human movements that can be used advantageously. In this thesis the virtual constraints approach is extended to a wider and rigorous use for analyzing, planning and reproducing human-like motions based on mathematical tools previously utilized for very particular control problems. It is often the case that some desired motions cannot be achieved by the robot due to limitations in available actuation power. This constraint rises the question of how to modify the mechanical design in order to achieve better performance. An underactuated planar two-link robot is used to demonstrate that springs can complement the actuation in parallel to an ordinary motor. Motion planning is carried out for the original robot dynamics while the springs are treated as part of the control action with a torque profile suited to the preplanned trajectory. Another issue discussed in this thesis is to find stable and unstable (hybrid) limit cycles for passive dynamic walking robots without integrating the full set of differential equations. Such procedure is demonstrated for the compass-gait biped by means of optimization with a reduced number of initial conditions and parameters to search. The properties of virtual constraints and reduced dynamics are exploited to solve this problem.

Motion planning and control synthesis are challenging problems for underactuated mechanical systems due to the presence of passive (non-actuated) degrees of freedom. For those systems that are additionally not feedback linearizable and with unstable internal dynamics there are no generic methods for planning trajectories and their feedback stabilization. For fully actuated mechanical systems, on the other hand, there are standard tools that provide a tractable solution. Still, the problem of generating efficient and optimal trajectories is nontrivial due to actuator limitations and motion-dependent velocity and acceleration constraints that are typically present. It is especially challenging for manipulators with kinematic redundancy. A generic approach for solving the above-mentioned problems is described in this work. We explicitly use the geometry of the state space of the mechanical system so that a synchronization of the generalized coordinates can be found in terms of geometric relations along the target motion with respect to a path coordinate. Hence, the time evolution of the state variables that corresponds to the target motion is determined by the system dynamics constrained to these geometrical relations, known as virtual holonomic constraints. Following such a reduction for underactuated mechanical systems, we arrive at integrable second-order dynamics associated with the passive degrees of freedom. Solutions of this reduced dynamics, together with the geometric relations, can be interpreted as a motion generator for the full system. For fully actuated mechanical systems the virtually constrained dynamics provides a tractable way of shaping admissible trajectories. Once a feasible target motion is found and the corresponding virtual holonomic constraints are known, we can describe dynamics transversal to the orbit in the state space and analytically compute a transverse linearization. This results in a linear time-varying control system that allows us to use linear control theory for achieving orbital stabilization of the nonlinear mechanical system as well as to conduct system analysis in the vicinity of the motion. The approach is applicable to continuous-time and impulsive mechanical systems irrespective of the degree of underactuation. The main contributions of this thesis are analysis of human movement regarding a nominal behavior for repetitive tasks, gait synthesis and stabilization for dynamic walking robots, and description of a numerical procedure for generating and stabilizing efficient trajectories for kinematically redundant manipulators.

Nature and its variety of motion forms have inspired new robot designs with inherentunderactuated dynamics. The fundamental characteristic of these controlled mechanicalsystems, called underactuated, is to have the number of actuators less than the number ofdegrees of freedom. The absence of full actuation brings challenges to planning feasibletrajectories and designing controllers. This is in contrast to classical fully-actuated robots.A particular problem that arises upon study of such systems is that of generating periodicmotions, which can be seen in various natural actions such as walking, running,hopping, dribbling a ball, etc. It is assumed that dynamics can be modeled by a classicalset of second-order nonlinear differential equations with impulse effects describing possibleinstantaneous impacts, such as the collision of the foot with the ground at heel strikein a walking gait. Hence, we arrive at creating periodic solutions in underactuated Euler-Lagrange systems with or without impulse effects. However, in the qualitative theory ofnonlinear dynamical systems, the problem of verifying existence of periodic trajectoriesis a rather nontrivial subject.The aim of this work is to propose systematic procedures to plan such motions and ananalytical technique to design orbitally stabilizing feedback controllers. We analyze andexemplify both cases, when the robotmodel is described just by continuous dynamics, andwhen continuous dynamics is interrupted from time to time by state-dependent updates.For trajectory planning, systems with one or two passive links are considered, forwhich conditions are derived to achieve periodicmotions by encoding synchronizedmovementsof all the degrees of freedom. For controller design we use an explicit form tolinearize dynamics transverse to the motion. This computation is valid for an arbitrarydegree of under-actuation. The linear system obtained, called transverse linearization, isused to analyze local properties in a vicinity of the motion, and also to design feedbackcontrollers. The theoretical background of these methods is presented, and developedin detail for some particular examples. They include the generation of oscillations forinverted pendulums, the analysis of human movements by captured motion data, and asystematic gait synthesis approach for a three-link biped walker with one actuator.