Robust Data-Driven Zero-Velocity Detection for Foot-Mounted Inertial Navigation

We present two novel techniques for detecting zero-velocity events to improve foot-mounted inertial navigation. Our first technique augments a classical zero-velocity detector by incorporating a motion classifier that adaptively updates the detector's threshold parameter. Our second technique uses a long short-term memory (LSTM) recurrent neural network to classify zero-velocity events from raw inertial data, in contrast to the majority of zero-velocity detection methods that rely on basic statistical hypothesis testing. We demonstrate that both of our proposed detectors achieve higher accuracies than existing detectors for trajectories including walking, running, and stair-climbing motions. Additionally, we present a straightforward data augmentation method that is able to extend the LSTM-based model to different inertial sensors without the need to collect new training data.

Inverse Kinematics for Serial Kinematic Chains via Sum of Squares Optimization

Inverse kinematics is a fundamental problem for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for serial kinematic chains is a difficult nonlinear problem, for which closed form solutions cannot be easily obtained. Therefore, computationally efficient numerical methods that can be adapted to a general class of manipulators are of great importance. % to motion planning and workspace generation tasks. In this paper, we use convex optimization techniques to solve the inverse kinematics problem with joint limit constraints for highly redundant serial kinematic chains with spherical joints in two and three dimensions. This is accomplished through a novel formulation of inverse kinematics as a nearest point problem, and with a fast sum of squares solver that exploits the sparsity of kinematic constraints for serial manipulators. Our method has the advantages of post-hoc certification of global optimality and a runtime that scales polynomialy with the number of degrees of freedom. Additionally, we prove that our convex relaxation leads to a globally optimal solution when certain conditions are met, and demonstrate empirically that these conditions are common and represent many practical instances. Finally, we provide an open source implementation of our algorithm.

Fast Manipulability Maximization Using Continuous-Time Trajectory Optimization

A significant challenge in manipulation motion planning is to ensure agility in the face of unpredictable changes during task execution. This requires the identification and possible modification of suitable joint-space trajectories, since the joint velocities required to achieve a specific end-effector motion vary with manipulator configuration. For a given manipulator configuration, the joint space-to-task space velocity mapping is characterized by a quantity known as the manipulability index. In contrast to previous control-based approaches, we examine the maximization of manipulability during planning as a way of achieving adaptable and safe joint space-to-task space motion mappings in various scenarios. By representing the manipulator trajectory as a continuous-time Gaussian process (GP), we are able to leverage recent advances in trajectory optimization to maximize the manipulability index during trajectory generation. Moreover, the sparsity of our chosen representation reduces the typically large computational cost associated with maximizing manipulability when additional constraints exist. Results from simulation studies and experiments with a real manipulator demonstrate increases in manipulability, while maintaining smooth trajectories with more dexterous (and therefore more agile) arm configurations.

Sparse Bounded Degree Sum of Squares Optimization for Certifiably Globally Optimal Rotation Averaging

Estimating unknown rotations from noisy measurements is an important step in SfM and other 3D vision tasks. Typically, local optimization methods susceptible to returning suboptimal local minima are used to solve the rotation averaging problem. A new wave of approaches that leverage convex relaxations have provided the first formal guarantees of global optimality for state estimation techniques involving SO(3). However, most of these guarantees are only applicable when the measurement error introduced by noise is within a certain bound that depends on the problem instance's structure. In this paper, we cast rotation averaging as a polynomial optimization problem over unit quaternions to produce the first rotation averaging method that is formally guaranteed to provide a certifiably globally optimal solution for \textit{any} problem instance. This is achieved by formulating and solving a sparse convex sum of squares (SOS) relaxation of the problem. We provide an open source implementation of our algorithm and experiments, demonstrating the benefits of our globally optimal approach.

Probabilistic Regression of Rotations using Quaternion Averaging and a Deep Multi-Headed Network

Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on prior work and argue that a multi-headed network structure we name HydraNet provides better calibrated uncertainty estimates than methods that rely on stochastic forward passes. Second, we extend HydraNet to targets that belong to the rotation group, SO(3), by regressing unit quaternions and using the tools of rotation averaging and uncertainty injection onto the manifold to produce three-dimensional covariances. Finally, we present results and analysis on a synthetic dataset, learn consistent orientation estimates on the 7-Scenes dataset, and show how we can use our learned covariances to fuse deep estimates of relative orientation with classical stereo visual odometry to improve localization on the KITTI dataset.

Learning Matchable Colorspace Transformations for Long-term Metric Visual Localization

Long-term metric localization is an essential capability of autonomous mobile robots, but remains challenging for vision-based systems in the presence of appearance change caused by lighting, weather or seasonal variations. While experience-based mapping has proven to be an effective technique for enabling visual localization across appearance change, the number of experiences required for reliable long-term localization can be large, and methods for reducing the necessary number of experiences are desired. Taking inspiration from physics-based models of color constancy, we propose a method for learning a nonlinear mapping from RGB to grayscale colorspaces that maximizes the number of feature matches for images captured under varying lighting and weather conditions. Our key insight is that useful image transformations can be learned by approximating conventional non-differentiable localization pipelines with a differentiable learned model that can predict a convenient measure of localization quality, such as the number of feature matches, for a given pair of images. Moreover, we find that the generality of appearance-robust RGB-to-grayscale mappings can be improved by incorporating a learned low-dimensional context feature computed for a specific image pair. Using synthetic and real-world datasets, we show that our method substantially improves feature matching across day-night cycles and presents a viable strategy for significantly improving the efficiency of experience-based visual localization.

The Phoenix Drone: An Open-Source Dual-Rotor Tail-Sitter Platform for Research and Education

In this paper, we introduce the Phoenix drone: the first completely open-source tail-sitter micro aerial vehicle (MAV) platform. The vehicle has a highly versatile, dual-rotor design and is engineered to be low-cost and easily extensible/modifiable. Our open-source release includes all of the design documents, software resources, and simulation tools needed to build and fly a high-performance tail-sitter for research and educational purposes. The drone has been developed for precision flight with a high degree of control authority. Our design methodology included extensive testing and characterization of the aerodynamic properties of the vehicle. The platform incorporates many off-the-shelf components and 3D-printed parts, in order to keep the cost down. Nonetheless, the paper includes results from flight trials which demonstrate that the vehicle is capable of very stable hovering and accurate trajectory tracking. Our hope is that the open-source Phoenix reference design will be useful to both researchers and educators. In particular, the details in this paper and the available open-source materials should enable learners to gain an understanding of aerodynamics, flight control, state estimation, software design, and simulation, while experimenting with a unique aerial robot.

Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion

We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system.