Dynamic state estimation for mobile robots

Abstract

The scientific goal of this thesis is to tackle different approaches for effective state estimation and modelling of relevant problems in the context of mobile robots. The starting point of this dissertation is the concept of probabilistic robotics, an emerging paradigm that combines state-of-the-art methods with the classic probabilistic theory, developing stochastic frameworks for understanding the uncertain nature of the interaction between a robot and its environment. This allows introducing relevant concepts which are the foundation of the localisation system implemented on the main experimental platform used on this dissertation. An accurate estimation of the position of a robot with respect to a fixed frame is fundamental for building navigation systems that can work in dynamic unstructured environments. This development also allows introducing additional contributions related with global localisation, dynamic obstacle avoidance, path planning and position tracking problems.

Kinematics on generalised manipulators are characterised for dealing with complex nonlinear systems. Nonlinear formulations are needed to properly model these systems, which are not always suitable for real-time realisation, lacking analytic formulations in most cases. In this context, this thesis tackles the serial-parallel dual kinematic problem with a novel approach, demonstrating state-of-the-art accuracy and real-time performance. With a spatial decomposition method, the forward kinematics problem on parallel robots and the inverse kinematics problem on serial manipulators is solved modelling the nonlinear behaviour of the pose space using Support Vector Machines. The results are validated on different topologies with the analytic solution for such manipulators, which demonstrates the applicability of the proposed method.

Modelling and control of complex dynamical systems is another relevant field with applications on mobile robots. Nonlinear techniques are usually applied to tackle problems like feature or object tracking. However, some nonlinear integer techniques applied for tasks like position tracking in mobile robots with complex dynamics have limited success when modelling such systems. Fractional calculus has demonstrated to be suitable to model complex processes like viscoelasticity or super diffusion. These tools, that take advantage of the generalization of the derivative and integral operators to a fractional order, have been applied to model and control different topics related with robotics in recent years with remarkable success.

With the proposal of a fractional-order PI controller, a suitable controller design method is presented to solve the position tracking problem. This is applied to control the distance of a self-driving car with respect to an objective, which can also be applied to other tracking applications like following a navigation path. Furthermore, this thesis introduces a novel fractional-order hyperchaotic system, stabilised with a full-pseudo-state-feedback controller and a located feedback method. This theoretical contribution of a chaotic system is introduced hoping to be useful in this context. Chaos theory has recently started to be applied to study manipulators, biped robots and autonomous navigation, achieving new and promising results, highlighting the uncertain and chaotic nature which also has been found on robots.

All together, this thesis is devoted to different problems related with dynamic state estimation for mobile robots, proposing specific contributions related with modelling and control of complex nonlinear systems. These findings are presented in the context of a self-driving electric car, Verdino, jointly developed in collaboration with the Robotics Group of Universidad de La Laguna (GRULL).