Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation

This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on approximations of the system dynamics, such as an Extended Kalman Filter (EKF), which uses a system's Jacobian linearization along the current best estimate of its trajectory. On the basis of the theory of invariant observer design by Barrau and Bonnabel, and in particular, the Invariant EKF (InEKF), we show that the error dynamics of the point contact-inertial system follows a log-linear autonomous differential equation; hence, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory. Due to the log-linear form of the error dynamics, it is not necessary to perform a nonlinear observability analysis to show that when using an Inertial Measurement Unit (IMU) and contact sensors, the absolute position of the robot and a rotation about the gravity vector (yaw) are unobservable. We further augment the state of the developed InEKF with IMU biases, as the online estimation of these parameters has a crucial impact on system performance. We evaluate the convergence of the proposed system with the commonly used quaternion-based EKF observer using a Monte-Carlo simulation. In addition, our experimental evaluation using a Cassie-series bipedal robot shows that the contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in the system dynamics.Comment: Published in the proceedings of Robotics: Science and Systems 201

Design and implementation of a relative localization system for ground and aerial robotic teams

The main focus of this thesis is to address the relative localization problem of a heterogenous team which comprises of both ground and micro aerial vehicle robots. This team configuration allows to combine the advantages of increased accessibility and better perspective provided by aerial robots with the higher computational and sensory resources provided by the ground agents, to realize a cooperative multi robotic system suitable for hostile autonomous missions. However, in such a scenario, the strict constraints in flight time, sensor pay load, and computational capability of micro aerial vehicles limits the practical applicability of popular map-based localization schemes for GPS denied navigation. Therefore, the resource limited aerial platforms of this team demand simpler localization means for autonomous navigation. Relative localization is the process of estimating the formation of a robot team using the acquired inter-robot relative measurements. This allows the team members to know their relative formation even without a global localization reference, such as GPS or a map. Thus a typical robot team would benefit from a relative localization service since it would allow the team to implement formation control, collision avoidance, and supervisory control tasks, independent of a global localization service. More importantly, a heterogenous team such as ground robots and computationally constrained aerial vehicles would benefit from a relative localization service since it provides the crucial localization information required for autonomous operation of the weaker agents. This enables less capable robots to assume supportive roles and contribute to the more powerful robots executing the mission. Hence this study proposes a relative localization-based approach for ground and micro aerial vehicle cooperation, and develops inter-robot measurement, filtering, and distributed computing modules, necessary to realize the system. The research study results in three significant contributions. First, the work designs and validates a novel inter-robot relative measurement hardware solution which has accuracy, range, and scalability characteristics, necessary for relative localization. Second, the research work performs an analysis and design of a novel nonlinear filtering method, which allows the implementation of relative localization modules and attitude reference filters on low cost devices with optimal tuning parameters. Third, this work designs and validates a novel distributed relative localization approach, which harnesses the distributed computing capability of the team to minimize communication requirements, achieve consistent estimation, and enable efficient data correspondence within the network. The work validates the complete relative localization-based system through multiple indoor experiments and numerical simulations. The relative localization based navigation concept with its sensing, filtering, and distributed computing methods introduced in this thesis complements system limitations of a ground and micro aerial vehicle team, and also targets hostile environmental conditions. Thus the work constitutes an essential step towards realizing autonomous navigation of heterogenous teams in real world applications

Characterisation and State Estimation of Magnetic Soft Continuum Robots

Minimally invasive surgery has become more popular as it leads to less bleeding, scarring, pain, and shorter recovery time. However, this has come with counter-intuitive devices and steep surgeon learning curves. Magnetically actuated Soft Continuum Robots (SCR) have the potential to replace these devices, providing high dexterity together with the ability to conform to complex environments and safe human interactions without the cognitive burden for the clinician. Despite considerable progress in the past decade in their development, several challenges still plague SCR hindering their full realisation. This thesis aims at improving magnetically actuated SCR by addressing some of these challenges, such as material characterisation and modelling, and sensing feedback and localisation. Material characterisation for SCR is essential for understanding their behaviour and designing effective modelling and simulation strategies. In this work, the material properties of commonly employed materials in magnetically actuated SCR, such as elastic modulus, hyper-elastic model parameters, and magnetic moment were determined. Additionally, the effect these parameters have on modelling and simulating these devices was investigated. Due to the nature of magnetic actuation, localisation is of utmost importance to ensure accurate control and delivery of functionality. As such, two localisation strategies for magnetically actuated SCR were developed, one capable of estimating the full 6 degrees of freedom (DOFs) pose without any prior pose information, and another capable of accurately tracking the full 6-DOFs in real-time with positional errors lower than 4~mm. These will contribute to the development of autonomous navigation and closed-loop control of magnetically actuated SCR

Optimal Spatial-Temporal Triangulation for Bearing-Only Cooperative Motion Estimation

Vision-based cooperative motion estimation is an important problem for many multi-robot systems such as cooperative aerial target pursuit. This problem can be formulated as bearing-only cooperative motion estimation, where the visual measurement is modeled as a bearing vector pointing from the camera to the target. The conventional approaches for bearing-only cooperative estimation are mainly based on the framework distributed Kalman filtering (DKF). In this paper, we propose a new optimal bearing-only cooperative estimation algorithm, named spatial-temporal triangulation, based on the method of distributed recursive least squares, which provides a more flexible framework for designing distributed estimators than DKF. The design of the algorithm fully incorporates all the available information and the specific triangulation geometric constraint. As a result, the algorithm has superior estimation performance than the state-of-the-art DKF algorithms in terms of both accuracy and convergence speed as verified by numerical simulation. We rigorously prove the exponential convergence of the proposed algorithm. Moreover, to verify the effectiveness of the proposed algorithm under practical challenging conditions, we develop a vision-based cooperative aerial target pursuit system, which is the first of such fully autonomous systems so far to the best of our knowledge

A Novel Case of Practical Exponential Observer Using Extended Kalman Filter

This technical note presents a case of practical exponential observer using extended Kalman filter (EKF) independent of certain restrictions, such as online check and estimation error of initial state. Recursive state estimation is usually a challenge for discrete-time nonlinear system in terms of computation cost. EKF is attractive with its simplicity since it is considered as an exponential observer given the above restrictions. However, those restrictions are so mathematically complicated that EKF cannot be practical in estimation. A novel case for an exponential observer using EKF is proposed, which is independent of such restrictions. However, these restrictions are proved to be unnecessary in the case. The proposed case is illustrated by a navigation system scenario. The validity of the case is demonstrated by a numerical simulation experiment. The system is deterministic