Trajectories of a rigid body are considered where the centre of the body is fixed or moves over any space form (that is, a sphere of any radius, the equivalent with negative curvature, and fiat 3D space). Open loop controls maintain the required trajectory. Three applications illustrate the concepts developed in the thesis. Firstly, a symmetric body moves over a sphere to any position and attitude where one torque maintains a constant rotation. The integration is achieved by specializing the double cover formulation of a rotation over any space form and by using a Lax pair consisting of the Hamiltonian and momentum vectors expressed in the same frame of reference. Secondly, an asymmetric satellite follows a planned trajectory to its target attitude. The natural rotation of an asymmetric satellite cannot be expressed analytically so two simple rotation modes are used; an eigenaxis and a spin stabilized rotation (with optimized spin rate). The profile of the angular velocity is adjusted by reparameterizing time to accelerate and stop the satellite. The controls required for this are compared with those required to maintain the planned rotation. In the final application, a search pattern of linear runs and turns is planned for an Autonomous Underwater Vehicle (AUV) which moves at an oblique angle. Thrusts and torques exerted by the AUV provide the controls to overcome drift, dissipative forces, conservative forces and to accelerate the surrounding fiuid out of the way. The latter consideration changes the effective inertia in different directions and the centre of mass of the AUV. Drift arises from the conservation of momentum and its evaluation is dependent on maintaining a constant inertia matrix along the trajectory. Dissipative forces are expressed in a generalized format applicable to other situations, such as aircraft and vehicles which do not have a preferred direction. In addition, the velocity profile is adjusted to smoothly join the linear run to the turn without coming to rest. The controls required to achieve this search pattern are determined.

Artificial Potential Fields (APFs) are a local motion planning technique widely used in the field of robotics. The use of this reactive technique has surged due to the production of advanced robots, which are ever increasingly being deployed in dynamic and unknown environments. However, the success of this approach is limited due to inherent local minima issues. While improved APF-based methods have been developed for the motion planning of mobile robots, for more complex robots such as robotic manipulators, the existing APF approaches are still limited. Thus, the specific aim of this thesis is to develop improved APF motion planning techniques for manipulators. Firstly, the common types of local minima specific to manipulator applications are defined. These are then addressed by combining APF functions with novel motion planning techniques, including a goal configuration sampling algorithm and a subgoal selection algorithm based on expanded convex hulls. These algorithms are used to identify the final configurations which solve the motion planning problem and subsequently plot a collision-free path, around any locally detected obstacles, to reach one of the valid goal configurations. This intelligent motion planning overcomes the naivety of the APF approach, assisting it to avoid the inherent local minima problems. This results in an APF-based motion planner which significantly improves on the existing APF( approach for manipulators. Additionally, the motion planning of dual-manipulator systems is also investigated. The proposed single manipulator motion planner is extended to solve two unique decoupled motion planning problems. While existing APF techniques for the cooperative motion planning of multiple mobile robots are used as inspiration to develop a novel APF-based motion planner which successfully solves fully-cooperative dual-arm motion planning tasks.

State estimation is a process of estimating the unmeasured or noisy states using the measured outputs and control inputs along with process and measurement models. The extended Kalman filter (EKF) has been an important approach for nonlinear state estimation over the last five decades. However, EKFs are only suitable for ‘mild’ nonlinearities where the first-order approximations of the nonlinear functions are available and they also require evaluation of state and measurement Jacobians at every iteration. This thesis presents a few linear and nonlinear state estimation methods and their applications. To start with, we investigate the use of the linear H∞ filter, which can deal with non-Gaussian noises, in a control application. The efficacy of the linear H∞ filter based sliding mode controller is verified on a quadruple tank system. The main tools for nonlinear state estimation are cubature Kalman filter (CKF) and its variants. A solution to simultaneous localisation and mapping (SLAM) problem using CKF is proposed. The effectiveness of the nonlinear CKF-SLAM over EKF- and UKF-SLAM is demonstrated. We propose a couple of new nonlinear state estimation algorithms, namely, cubature information filters (CIFs) and cubature H∞ filters (CH∞Fs), and their square root versions. The CIF is derived from an extended information filter and a CKF. The CIF is further extended for use in multi-sensor state estimation and its square root version is derived using a unitary transformation. For non-linear and non-Gaussian systems, we fuse an extended H∞ filter and CKF to form CH∞F which has the desirable features of both CKF and an extended H∞ filter. Further, we derive a square root CH∞F using a J-unitary transformation for numerical stability. The efficacies of the proposed algorithms are evaluated on simulation examples.

This thesis is submitted by D. P. Atherton, B. Eng. to the Victoria University of Manchester for the degree of Doctor of Philosophy. The work for the thesis was carried out in the Servomechanisms Laboratory in the E1ecttica1 Engineering Department of the University during the period October 1956 to June 1962. The thesis discusses the analysis of non-linear feedback systems with multiple inputs. In the first part, various methods are presented for evaluating the response of non-linear characteristics to several input signals, particular emphasis being placed on the concept and evaluation of modified non-linear characteristics. Experimental results and practical applications of the theory _ are given. The assessment of the stability and the evaluation of the response of non-linear feedback systems with multiple inputs is considered in part II together with the possibility of signal modification of the response of non-linear systems. Various analogue circuits and simulation techniques employed are given in part III.

A key motive of human-robot interaction is to make robots and humans interact through different aspects of the real world. As robots become more and more realistic in appearance, so has the desire for them to exhibit complex behaviours. A growing area of interest in terms of complex behaviour is robot dancing. Dance is an entertaining activity that is enjoyed either by being the performer or the spectator. Each dance contain fundamental features that make-up a dance. It is the curiosity for some researchers to model such an activity for robots to perform in human social environments. From current research, most dancing robots are pre-programmed with dance motions and few have the ability to generate their own dance or alter their movements according to human responses while dancing. This thesis explores the question Can a robot learn to dance? . A dancing framework is proposed to address this question. The Sarsa algorithm and the Softmax algorithm from traditional reinforcement learning form part of the dancing framework to enable a virtual robot learn and adapt to appropriate dance behaviours. The robot follows a progressive approach, utilising the knowledge obtained at each stage of its development to improve the dances that it generates. The proposed framework addresses three stages of development of a robot s dance: learning ability; creative ability of dance motions, and adaptive ability to human preferences. Learning ability is the ability to make a robot gradually perform the desired dance behaviours. Creative ability is the idea of the robot generating its own dance motions, and structuring them into a dance. Adaptive ability is where the robot changes its dance in response to human feedback. A number of experiments have been conducted to explore these challenges, and verified that the quality of the robot dance can be improved through each stage of the robot s development.

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In this work certain kinds of distributed parameter optimal control problem are considered, governed by non-linear partial differential equations of parabolic and hyperbolic type. Conditions necessary for optimality are developed. These are used to derive a range of numerical algorithms for solution of the control problem. Also described is an algorithm searching directly on the performance index, without requiring satisfaction of the necessary conditions. Five system examples exhibiting a wide range of distributed parameter system features are analysed using the different numerical methods and results are compared. A general discussion of the main characteristics' of the algorithms is given.

Social insects have inspired the behaviours of swarm robotic systems for the last 20 years. Interactions of the simple individuals in these swarms form solutions to relatively complex problems. A novel swarm robotic method is investigated for future robotic cooperative object recognition tasks. Previous multi-agent systems involve cameras and image analyses to identify objects. They cooperate only to improve their hypotheses of the shape's identity. The system proposed uses agents whose interactions with each other around the physical boundaries of the object's shape allow the distinguishing features found. The agents are a physical embodiment of the vision system, making them suitable for environments where it would not be possible to use a camera. A Simplified Hexagonal Model was developed to simulate and examine the strategies. The hexagonal cells of which can be empty, contain an agent (hBot) or part of an object shape. Initially the hBots are required to identify the valid object shapes from a set of two types of known shapes. To do this the hBots change state when in contact with an object and when touching other hBots of the same state level, where some states are only achieved when neighbouring certain object shapes. The agents are oblivious, anonymous and homogeneous. They also do not know their position or orientation and cannot distinguish between object shapes alone due to their limited sensor range. Further work increased the number of object shapes to provide a range of scenarios. In order to hypothesise the difficulty a swarm of hBots has distinguishing one object shape type from any other a system is devised to compare object shapes. Data-chains describe the object shapes, without orientation, by considering how many object cells the empty cells surrounding them are in contact with. Pairs of object shapes could then be analysed to determine their difference value from each other. These difference values correlate to a swarms difficulty in completing the specific scenarios. Finally, a genetic algorithm (GA) was analysed as a method to determine the behaviours of the hBots different states. The GA is more efficient than both derived and randomly populated methods, showing that a GA can be used to train agents without first determining differences between the object shapes. These insights provide a significant contribution to knowledge through the object shape analyses method and the swarm robotic strategies which establish a unique foundation for further development of novel applications for both swarm robotic and cooperative object recognition research.