State Estimation for a Humanoid Robot

This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in [1] on a quadruped platform by incorporating the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter (EKF) accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. The filter employs a sensor-based prediction model which uses inertial data from an IMU and corrects for integrated error using a kinematics-based measurement model which relies on joint encoders and a kinematic model to determine the relative position and orientation of the feet. A nonlinear observability analysis is performed on both the original and updated filters and it is concluded that the new filter significantly simplifies singular cases and improves the observability characteristics of the system. Results on simulated walking and squatting datasets demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.Comment: IROS 2014 Submission, IEEE/RSJ International Conference on Intelligent Robots and Systems (2014) 952-95

Dense RGB-D-Inertial SLAM with Map Deformations

While dense visual SLAM methods are capable of estimating dense reconstructions of the environment, they suffer from a lack of robustness in their tracking step, especially when the optimisation is poorly initialised. Sparse visual SLAM systems have attained high levels of accuracy and robustness through the inclusion of inertial measurements in a tightly-coupled fusion. Inspired by this performance, we propose the first tightly-coupled dense RGB-D-inertial SLAM system. Our system has real-time capability while running on a GPU. It jointly optimises for the camera pose, velocity, IMU biases and gravity direction while building up a globally consistent, fully dense surfel-based 3D reconstruction of the environment. Through a series of experiments on both synthetic and real world datasets, we show that our dense visual-inertial SLAM system is more robust to fast motions and periods of low texture and low geometric variation than a related RGB-D-only SLAM system.Comment: Accepted at IROS 2017; supplementary video available at https://youtu.be/-gUdQ0cxDh

A Primer on the Differential Calculus of 3D Orientations

The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal solutions. The existence of many different conventions further complicates this issue, especially when interfacing multiple differing implementations. This document discusses an alternative approach which makes use of a more abstract notion of 3D orientations. The relative orientation between two coordinate systems is primarily identified by the coordinate mapping it induces. This is combined with the standard exponential map in order to introduce representation-independent and minimal differentials, which are very convenient in optimization based methods

Why and How to Avoid the Flipped Quaternion Multiplication

Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to exchanging formulas or implementations: there are two quaternion multiplications in common use, Hamilton's original multiplication and its flipped version, which is often associated with NASA's Jet Propulsion Laboratory. We believe that this particular issue is completely avoidable and only exists today due to a lack of understanding. This paper explains the underlying problem for the popular passive world to body usage of rotation quaternions, and derives an alternative solution compatible with Hamilton's multiplication. Furthermore, it argues for entirely discontinuing the flipped multiplication. Additionally, it provides recipes for efficiently detecting relevant conventions and migrating formulas or algorithms between them.Comment: 16 pages, 1 figure, 2 tables (minor improvements and fixes over v1, smaller page margins