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.

Generating and stabilizing periodic motions in nonlinear systems is a challenging task. In the control system community this topic is also known as limit cycle control. In recent years a framework known as Virtual Holonomic Constraints (VHC) has been developed as one of the solutions to this problem. The aim of this thesis is to give an insight into this approach and its practical application. The contribution of this work is primarily the experimental validation of the theory. A step by step procedure of this methodology is given for motion planning, as well as for controller design. Three particular setups were chosen for experiments: the inertia wheel pendulum, the Furuta pendulum and the two-link planar pendulum. These under-actuated mechanical systems are well known benchmarking setups for testing advanced control design methods. Further application is intended for cases such as biped robot walking/running, human and animal locomotion analysis, etc.

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As vehicles become electrified and more intelligent in terms of sensing, actuation and processing; a number of interesting possibilities arise in controlling vehicle dynamics and driving behavior. Over-actuation with inwheel motors, all wheel steering and active camber is one such possibility, and can facilitate control combinations that push boundaries in energy consumption and safety. Optimal control can be used to investigate the best combinations of control inputs to an over-actuated system. In Part 1, a literature study is performed on the state of art in the field of optimal control, highlighting the strengths and weaknesses of different methods and their applicability to a vehicular system. Out of these methods, Dynamic Programming and Model Predictive Control are of particular interest. Prior work in overactuation, as well as control for reducing tire energy dissipation is studied, and utilized to frame the dynamics, constraints and objective of an optimal control problem. In Part 2, an optimal control problem representing the lateral dynamics of an over-actuated vehicle is formulated, and solved for different objectives using Dynamic Programming. Simulations are performed for standard driving maneuvers, performance parameters are defined, and a system design study is conducted. Objectives include minimizing tire cornering resistance (saving energy) and maintaining the reference vehicle trajectory (ensuring safety), and optimal combinations of input steering and camber angles are derived as a performance benchmark. Following this, Model Predictive Control is used to design an online controller that follows the optimal vehicle state, and studies are performed to assess the suitability of MPC to over-actuation. Simulation models are also expanded to include non-linear tires. Finally, vehicle implementation is considered on the KTH Research Concept Vehicle (RCV) and four vehicle-implementable control cases are presented. To conclude, this thesis project uses methods in optimal control to find candidate solutions to improve vehicle performance thanks to over-actuation. Extensive vehicle tests are needed for a clear indication of the energy saving achievable, but simulations show promising performance improvements for vehicles overactuated with all-wheel steering and active camber.