Gaussian processes for information-theoretic robotic mapping and exploration

University of Technology Sydney. Faculty of Engineering and Information Technology.This thesis proposes a framework for autonomous robotic mapping, exploration, and planning that uses Gaussian Processes (GPs) to model high-dimensional dense maps and solve the problem of infinite-horizon planning with imperfect state information. Robotic exploration is traditionally implemented using occupancy grid representations and geometric targets known as frontiers. The occupancy grid representation relies on the assumption of independence between grid cells and ignores structural correlations present in the environment. We develop an incremental GP occupancy mapping technique that is computationally tractable for online map building and represents a continuous model of uncertainty over the map spatial coordinates. The standard way to represent geometric frontiers extracted from occupancy maps is to assign binary values to each grid cell. We extend this notion to novel probabilistic frontier maps computed efficiently using the gradient of the GP occupancy map and propose a mutual information-based greedy exploration technique built on that representation. A primary motivation is the fact that high-dimensional map inference requires fewer observations, leading to a faster map entropy reduction during exploration for map building scenarios. The uncertainty from pose estimation is often ignored during current mapping strategies as the dense belief representation of occupancy maps makes the uncertainty propagation impractical. Additionally, when kernel methods are applied, such maps tend to model structural shapes of the environment with excessive smoothness. We show how the incremental GP occupancy mapping technique can be extended to accept uncertain robot poses and mitigate the excessive smoothness problem using Warped Gaussian Processes. This approach can model non-Gaussian noise in the observation space and capture the possible non-linearity in that space better than standard GPs. Finally, we develop a sampling-based information gathering planner, with an information-theoretic convergence, which allows dense belief representations. The planner takes the present uncertainty in state estimation into account and provides a general framework for robotic exploration in a priori unknown environments with an information-theoretic stopping criterion. The developed framework relaxes the need for any state or action space discretization and is a fully information-driven integrated navigation technique. The developed framework can be applied to a large number of scenarios where the robot is tasked to perform exploration and information gathering simultaneously. The developed algorithms in this thesis are implemented and evaluated using simulated and experimental datasets and are publicly available as open source libraries

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

Exploration on continuous Gaussian process frontier maps

An information-driven autonomous robotic explo- ration method on a continuous representation of unknown envi- ronments is proposed in this paper. The approach conveniently handles sparse sensor measurements to build a continuous model of the environment that exploits structural dependencies without the need to resort to a fixed resolution grid map. A gradient field of occupancy probability distribution is regressed from sensor data as a Gaussian process providing frontier boundaries for further exploration. The resulting continuous global frontier surface completely describes unexplored regions and, inherently, provides an automatic stop criterion for a desired sensitivity. The performance of the proposed approach is evaluated through simulation results in the well-known Freiburg and Cave maps.Peer ReviewedPostprint (author’s final draft

4D Panoptic Segmentation as Invariant and Equivariant Field Prediction

In this paper, we develop rotation-equivariant neural networks for 4D panoptic segmentation. 4D panoptic segmentation is a recently established benchmark task for autonomous driving, which requires recognizing semantic classes and object instances on the road based on LiDAR scans, as well as assigning temporally consistent IDs to instances across time. We observe that the driving scenario is symmetric to rotations on the ground plane. Therefore, rotation-equivariance could provide better generalization and more robust feature learning. Specifically, we review the object instance clustering strategies, and restate the centerness-based approach and the offset-based approach as the prediction of invariant scalar fields and equivariant vector fields. Other sub-tasks are also unified from this perspective, and different invariant and equivariant layers are designed to facilitate their predictions. Through evaluation on the standard 4D panoptic segmentation benchmark of SemanticKITTI, we show that our equivariant models achieve higher accuracy with lower computational costs compared to their non-equivariant counterparts. Moreover, our method sets the new state-of-the-art performance and achieves 1st place on the SemanticKITTI 4D Panoptic Segmentation leaderboard

Hybrid Contact Preintegration for Visual-Inertial-Contact State Estimation Using Factor Graphs

The factor graph framework is a convenient modeling technique for robotic state estimation where states are represented as nodes, and measurements are modeled as factors. When designing a sensor fusion framework for legged robots, one often has access to visual, inertial, joint encoder, and contact sensors. While visual-inertial odometry has been studied extensively in this framework, the addition of a preintegrated contact factor for legged robots has been only recently proposed. This allowed for integration of encoder and contact measurements into existing factor graphs, however, new nodes had to be added to the graph every time contact was made or broken. In this work, to cope with the problem of switching contact frames, we propose a hybrid contact preintegration theory that allows contact information to be integrated through an arbitrary number of contact switches. The proposed hybrid modeling approach reduces the number of required variables in the nonlinear optimization problem by only requiring new states to be added alongside camera or selected keyframes. This method is evaluated using real experimental data collected from a Cassie-series robot where the trajectory of the robot produced by a motion capture system is used as a proxy for ground truth. The evaluation shows that inclusion of the proposed preintegrated hybrid contact factor alongside visual-inertial navigation systems improves estimation accuracy as well as robustness to vision failure, while its generalization makes it more accessible for legged platforms.Comment: Detailed derivations are provided in the supplementary material document listed under "Ancillary files

Exploration using an information-based reaction-diffusion process

Trabajo presentado al ACRA 2013 celebrado en Sidney del 2 al 4 de diciembre.In this paper, a novel solution for autonomous robotic exploration is proposed. We model the distribution of information in an unknown environment as an unsteady diffusion process, which can be an appropriate mathematical formulation and analogy for expanding, time-varying, and dynamic environments. This information distribution map is the solution of the diffusion process partial differential equation, and is regressed from sensor data as a Gaussian Process. Optimization of the process parameters leads to an optimal frontier map which describes regions of interest for further exploration. Since the presented approach considers a continuous model of the environment, it can be used to plan smooth exploration paths exploiting the structural dependencies of the environment whilst handling sparse sensor measurements. The performance of the approach is evaluated through simulation results in the well-known Freiburg and Cave maps.J. Andrade acknowledges support from the Spanish Ministry of Economy and Competitiveness project PAU+ DPI 2011-27510 and the EU FP7 project ARCAS ICT-287617. R. Valencia acknowledges support from the EU FP7 project SPENCER ICT-600877.Peer Reviewe