Relative continuous-time SLAM

Appearance-based techniques for simultaneous localization and mapping (SLAM) have been highly successful in assisting robot-motion estimation; however, these vision-based technologies have long assumed the use of imaging sensors with a global shutter, which are well suited to the traditional, discrete-time formulation of visual problems. In order to adapt these technologies to use scanning sensors, we propose novel methods for both outlier rejection and batch nonlinear estimation. Traditionally, the SLAM problem has been formulated in a single-privileged coordinate frame, which can become computationally expensive over long distances, particularly when a loop closure requires the adjustment of many pose variables. Recent discrete-time estimators have shown that a completely relative coordinate framework can be used to incrementally find a close approximation of the full maximum-likelihood solution in constant time. In order to use scanning sensors, we propose moving the relative coordinate formulation of SLAM into continuous time by estimating the velocity profile of the robot. We derive the relative formulation of the continuous-time robot trajectory and formulate an estimator using temporal basis functions. A motion-compensated outlier rejection scheme is proposed by using a constant-velocity model for the random sample consensus algorithm. Our experimental results use intensity imagery from a two-axis scanning lidar; due to the sensors’ scanning nature, it behaves similarly to a slow rolling-shutter camera. Both algorithms are validated using a sequence of 6880 lidar frames acquired over a 1.1 km traversal.

Continuous-time batch trajectory estimation using temporal basis functions

Roboticists often formulate estimation problems in discrete time for the practical reason of keeping the state size tractable; however, the discrete-time approach does not scale well for use with high-rate sensors, such as inertial measurement units, rolling-shutter cameras, or sweeping laser imaging sensors. The difficulty lies in the fact that a pose variable is typically included for every time at which a measurement is acquired, rendering the dimension of the state impractically large for large numbers of measurements. This issue is exacerbated for the simultaneous localization and mapping problem, which further augments the state to include landmark variables. To address this tractability issue, we propose to move the full Maximum-a-Posteriori estimation problem into continuous time and use temporal basis functions to keep the state size manageable. We present a full probabilistic derivation of the continuous-time estimation problem, derive an estimator based on the assumption that the densities and processes involved are Gaussian and show how the coefficients of a relatively small number of basis functions can form the state to be estimated, making the solution efficient. Our derivation is presented in steps of increasingly specific assumptions, opening the door to the development of other novel continuous-time estimation algorithms through the application of different assumptions at any point. We use the simultaneous localization and mapping problem as our motivation throughout the paper, although the approach is not specific to this application. Results from two experiments are provided to validate the approach: (i) self-calibration involving a camera and a high-rate inertial measurement unit, and (ii) perspective localization with a rolling-shutter camera.

Vision-aided inertial navigation with rolling-shutter cameras

In this paper, we focus on the problem of pose estimation using measurements from an inertial measurement unit and a rolling-shutter (RS) camera. The challenges posed by RS image capture are typically addressed by using approximate, low-dimensional representations of the camera motion. However, when the motion contains significant accelerations (common in small-scale systems) these representations can lead to loss of accuracy. By contrast, we here describe a different approach, which exploits the inertial measurements to avoid any assumptions on the nature of the trajectory. Instead of parameterizing the trajectory, our approach parameterizes the errors in the trajectory estimates by a low-dimensional model. A key advantage of this approach is that, by using prior knowledge about the estimation errors, it is possible to obtain upper bounds on the modeling inaccuracies incurred by different choices of the parameterization’s dimension. These bounds can provide guarantees for the performance of the method, and facilitate addressing the accuracy–efficiency tradeoff. This RS formulation is used in an extended-Kalman-filter estimator for localization in unknown environments. Our results demonstrate that the resulting algorithm outperforms prior work, in terms of accuracy and computational cost. Moreover, we demonstrate that the algorithm makes it possible to use low-cost consumer devices (i.e. smartphones) for high-precision navigation on multiple platforms.