Fused Angles and the Deficiencies of Euler Angles

Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking bipedal robots, but have since found wider application due to their useful properties. A comparative analysis between fused angles and Euler angles is presented in this paper, delineating the specific differences between the two representations that make fused angles more suitable for representing orientations in balance-related scenarios. Aspects of comparison include the locations of the singularities, the associated parameter sensitivities, the level of mutual independence of the parameters, and the axisymmetry of the parameters.Comment: International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, 201

Tilt Rotations and the Tilt Phase Space

In this paper, the intuitive idea of tilt is formalised into the rigorous concept of tilt rotations. This is motivated by the high relevance that pure tilt rotations have in the analysis of balancing bodies in 3D, and their applicability to the analysis of certain types of contacts. The notion of a 'tilt rotation' is first precisely defined, before multiple parameterisations thereof are presented for mathematical analysis. It is demonstrated how such rotations can be represented in the so-called tilt phase space, which as a vector space allows for a meaningful definition of commutative addition. The properties of both tilt rotations and the tilt phase space are also extensively explored, including in the areas of spherical linear interpolation, rotational velocities, rotation composition and rotation decomposition.Comment: International Conference on Humanoid Robots (Humanoids), Beijing, China, 201

Omnidirectional Bipedal Walking with Direct Fused Angle Feedback Mechanisms

An omnidirectional closed-loop gait based on the direct feedback of orientation deviation estimates is presented in this paper. At the core of the gait is an open-loop central pattern generator. The orientation feedback is derived from a 3D nonlinear attitude estimator, and split into the relevant angular deviations in the sagittal and lateral planes using the concept of fused angles. These angular deviations from expected are used by a number of independent feedback mechanisms, including one that controls timing, to perform stabilising corrective actions. The tuning of the feedback mechanisms is discussed, including an LQR-based approach for tuning the transient sagittal response. The actuator control scheme and robot pose representations in use are also addressed. Experimental results on an igus Humanoid Open Platform demonstrate the core concept of this paper, that if the sensor management and feedback chains are carefully constructed, comparatively simple model-free and robot-agnostic feedback mechanisms can successfully stabilise a generic bipedal gait.Comment: International Conference on Humanoid Robots (Humanoids), Canc\'un, Mexico, 201

Fused Angles: A Representation of Body Orientation for Balance

The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a rotation have been developed over the years. Motivated by the task of representing the orientation of a balancing body, the fused angles parameterisation is developed and introduced in this paper. This novel representation is carefully defined both mathematically and geometrically, and thoroughly investigated in terms of the properties it possesses, and how it relates to other existing representations. A second intermediate representation, tilt angles, is also introduced as a natural consequence thereof.Comment: International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, 201

Robust Sensor Fusion for Robot Attitude Estimation

Knowledge of how a body is oriented relative to the world is frequently invaluable information in the field of robotics. An attitude estimator that fuses 3-axis gyroscope, accelerometer and magnetometer data into a quaternion orientation estimate is presented in this paper. The concept of fused yaw, used by the estimator, is also introduced. The estimator, a nonlinear complementary filter at heart, is designed to be uniformly robust and stable---independent of the absolute orientation of the body---and has been implemented and released as a cross-platform open source C++ library. Extensions to the estimator, such as quick learning and the ability to deal dynamically with cases of reduced sensory information, are also presented.Comment: International Conference on Humanoid Robots (Humanoids), Madrid, Spain, 201

Bipedal Walking with Corrective Actions in the Tilt Phase Space

Many methods exist for a bipedal robot to keep its balance while walking. In addition to step size and timing, other strategies are possible that influence the stability of the robot without interfering with the target direction and speed of locomotion. This paper introduces a multifaceted feedback controller that uses numerous different feedback mechanisms, collectively termed corrective actions, to stabilise a core keypoint-based gait. The feedback controller is experimentally effective, yet free of any physical model of the robot, very computationally inexpensive, and requires only a single 6-axis IMU sensor. Due to these low requirements, the approach is deemed to be highly portable between robots, and was specifically also designed to target lower cost robots that have suboptimal sensing, actuation and computational resources. The IMU data is used to estimate the yaw-independent tilt orientation of the robot, expressed in the so-called tilt phase space, and is the source of all feedback provided by the controller. Experimental validation is performed in simulation as well as on real robot hardware.Comment: International Conference on Humanoid Robots (Humanoids), Beijing, China, 201

Hierarchical and State-based Architectures for Robot Behavior Planning and Control

In this paper, two behavior control architectures for autonomous agents in the form of cross-platform C++ frameworks are presented, the State Controller Library and the Behavior Control Framework. While the former is state-based and generalizes the notion of states and finite state machines to allow for multi-action planning, the latter is behavior-based and exploits a hierarchical structure and the concept of inhibitions to allow for dynamic transitioning. The two frameworks have completely independent implementations, but can be used effectively in tandem to solve behavior control problems on all levels of granularity. Both frameworks have been used to control the NimbRo-OP, a humanoid soccer robot developed by team NimbRo of the University of Bonn.Comment: Proceedings of 8th Workshop on Humanoid Soccer Robots, International Conference on Humanoid Robots (Humanoids), Atlanta, USA, 201

Analytic Bipedal Walking with Fused Angles and Corrective Actions in the Tilt Phase Space

This work presents algorithms for the feedback-stabilised walking of bipedal humanoid robotic platforms, along with the underlying theoretical and sensorimotor frameworks required to achieve it. Bipedal walking is inherently complex and difficult to control due to the high level of nonlinearity and significant number of degrees of freedom of the concerned robots, the limited observability and controllability of the corresponding states, and the combination of imperfect actuation with less-than-ideal sensing. The presented methods deal with these issues in a multitude of ways, ranging from the development of an actuator control and feed-forward compensation scheme, to the inclusion of filtering in almost all of the gait stabilisation feedback pipelines. Two gaits are developed and investigated, the direct fused angle feedback gait, and the tilt phase controller. Both gaits follow the design philosophy of leveraging a semi-stable open-loop gait generator, and extending it through stabilising feedback via the means of so-called corrective actions. The idea of using corrective actions is to modify the generation of the open-loop joint waveforms in such a way that the balance of the robot is influenced and thereby ameliorated. Examples of such corrective actions include modifications of the arm swing and leg swing trajectories, the application of dynamic positional and rotational offsets to the hips and feet, and adjustments of the commanded step size and timing. Underpinning both feedback gaits and their corresponding gait generators are significant advances in the field of 3D rotation theory. These advances include the development of three novel rotation representations, the tilt angles, fused angles, and tilt phase space representations. All three of these representations are founded on a new innovative way of splitting 3D rotations into their respective yaw and tilt components.Comment: Extended version of PhD thesis (2020), 571 pages, 127 figures, 24 video

A Monocular Vision System for Playing Soccer in Low Color Information Environments

Humanoid soccer robots perceive their environment exclusively through cameras. This paper presents a monocular vision system that was originally developed for use in the RoboCup Humanoid League, but is expected to be transferable to other soccer leagues. Recent changes in the Humanoid League rules resulted in a soccer environment with less color coding than in previous years, which makes perception of the game situation more challenging. The proposed vision system addresses these challenges by using brightness and texture for the detection of the required field features and objects. Our system is robust to changes in lighting conditions, and is designed for real-time use on a humanoid soccer robot. This paper describes the main components of the detection algorithms in use, and presents experimental results from the soccer field, using ROS and the igus Humanoid Open Platform as a testbed. The proposed vision system was used successfully at RoboCup 2015.Comment: Proceedings of 10th Workshop on Humanoid Soccer Robots, International Conference on Humanoid Robots (Humanoids), Seoul, Korea, 201

NimbRo-OP2: Grown-up 3D Printed Open Humanoid Platform for Research

The versatility of humanoid robots in locomotion, full-body motion, interaction with unmodified human environments, and intuitive human-robot interaction led to increased research interest. Multiple smaller platforms are available for research, but these require a miniaturized environment to interact with---and often the small scale of the robot diminishes the influence of factors which would have affected larger robots. Unfortunately, many research platforms in the larger size range are less affordable, more difficult to operate, maintain and modify, and very often closed-source. In this work, we introduce NimbRo-OP2X, an affordable, fully open-source platform in terms of both hardware and software. Being almost 135cm tall and only 18kg in weight, the robot is not only capable of interacting in an environment meant for humans, but also easy and safe to operate and does not require a gantry when doing so. The exoskeleton of the robot is 3D printed, which produces a lightweight and visually appealing design. We present all mechanical and electrical aspects of the robot, as well as some of the software features of our well-established open-source ROS software. The NimbRo-OP2X performed at RoboCup 2017 in Nagoya, Japan, where it won the Humanoid League AdultSize Soccer competition and Technical Challenge.Comment: International Conference on Humanoid Robots (Humanoids), Birmingham, England, 201