Research presented in the dissertation is related to the design and integration of a control system for quadruped robot locomotion. The research is divided into three independent parts (adaptive compliance, kinematics and motion trajectory generation), which are integrated in one system with a main goal of achieving more natural and energy efficient quadruped robot locomotion. Adaptation of leg compliance with respect to the changes in ground stiffness and stride frequency proved to be essential in achieving energy optimal locomotion. To facilitate both compliance adaptation and maintaining the stability of locomotion, a control system needs to be able to detect the changes in the stiffness. This dissertation showcases a novel mechanical design of a compliant robot leg with both active and variable passive compliance. Additionally, the design allows for the detection of the changes in ground stiffness by measuring contact time from a feedback signal from the flex sensors mounted on the spiral feet. In order to achieve modular and robust quadruped robot control system it is important to approach to the single leg kinematics and the whole body kinematics separately. The single leg inverse kinematics problem in relation to hip or central body coordinate system is calculated analytically due to a limited number of degrees of freedom. On the other hand, the whole body position and orientation control in relation to a world coordinate system is performed by using the Jacobian matrix. Jacobian pseudoinverse with local null-space optimization enables the control system to utilize the redundancy of the robot and allows for definition of various optimization criteria (e.g. minimization of kinetic energy) or to aid in some additional task achievement (e.g. mass distribution control). Dynamic (cyclic) trajectory (walk, trot, gallop, ...) and static (acyclic) trajectory (getting up, lying down, sitting down...) motion sequence generation is performed in a local leg coordinate system by using the trajectories describing the motion of the foot. In order to obtain specific gait motion, all four leg trajectories are synchronized through a state machine. The presented control algorithm has ability to perform dynamic and static trajectories, provides controllable changes of motion sequences and ensures integration with the mentioned whole body kinematics. The experimental validation of the presented control system is carried out on four research platforms: three versions of electrically driven quadruped platforms, and the four-flipper tracks-driven mobile robot. The experiments have been performed in virtual and real environments. The first chapter gives an introduction into the field and research goals. The second chapter provides an overview of the existing mechanical robot leg designs with passive, active and hybrid compliance ability. A novel design of a quadruped robot is presented. Proposed novel legs have feet in the form of a spiral spring attached to the rotary shaft of the ankle. The fact that the spiral spring can rotate and change the contact angle with the ground extends the variable passive property to the leg in a whole and thus enables direct stiffness control during robot motion. Foot spring stiffness and damping are experimentally identified. The foot contact angle adaptation algorithm, based on a contact time feedback measurement by a flex sensor, is presented and tested on a single leg experimental platform. Chapter 3 gives an overview of the current state of the research in the area of velocity transform theory and introduces general central body kinematics model. The central body position and orientation control is performed by using the Jacobian matrix. Jacobian pseudoinverse with local null-space optimization uses robot's redundancy to define various optimization criteria (minimisation kinetic energy) or to aid in some additional task achievement (mass distribution control). The presented general central body kinematics model is implemented and tested on several quadruped platforms (Dynarobin v. 1, 2, and 3) and on the mobile robot for exploration and inspection (VIV). Chapter 4 defines general tasks for control system in terms of motion trajectory generation, as for dynamics trajectories (walk, trot, gallop, ...) with controllable gait switching ability, so for static trajectories (getting up, lying down, sitting down...). Two existing trajectory generation concepts are presented: central pattern generator based on coupled oscillators, and SIMBICON which is based on state machines. Improved trajectory generation concept based on a state machine with integrated central body kinematics is presented. The foot trajectories for all types of four-legged gaits are described as cyclic trajectories divided into three segments: propel, push and adjust. The presented control system is validated inside virtual environment. Chapter 5 deals with the presented control system experimentally validated on a real quadruped robot, version Dynarobin \#3. The experiments confirm that the presented control system can generate dynamic and static quadruped motion trajectories with the ability to simultaneously control the position and orientation of the body. This chapter also gives concluding remarks and provides guidelines for future work regarding energy efficient quadruped locomotion, robot stiffness adaptation to stiffness variations of natural uneven terrains, etc.