Timothy D. Barfoot’s research while affiliated with University of Toronto and other places

GNSS is unreliable, inaccurate, and insufficient in many real-time autonomous field applications. In this work, we present a GNSS-free global localization solution that contains a method of registering imaging radar on the ground with overhead RGB imagery, with joint optimization of relative poses from odometry and global poses from our overhead registration. Previous works have used various combinations of ground sensors and overhead imagery, and different feature extraction and matching methods. These include various handcrafted and deep-learning-based methods for extracting features from overhead imagery. Our work presents insights on extracting essential features from RGB overhead images for effective global localization against overhead imagery using only ground radar and a single georeferenced initial guess. We motivate our method by evaluating it on datasets in diverse geographic conditions and robotic platforms, including on an Unmanned Surface Vessel (USV) as well as urban and suburban driving datasets.

For several tasks, ranging from manipulation to inspection, it is beneficial for robots to localize a target object in their surroundings. In this paper, we propose an approach that utilizes coarse point clouds obtained from miniaturized VL53L5CX Time-of-Flight (ToF) sensors (tiny lidars) to localize a target object in the robot's workspace. We first conduct an experimental campaign to calibrate the dependency of sensor readings on relative range and orientation to targets. We then propose a probabilistic sensor model that is validated in an object pose estimation task using a Particle Filter (PF). The results show that the proposed sensor model improves the performance of the localization of the target object with respect to two baselines: one that assumes measurements are free from uncertainty and one in which the confidence is provided by the sensor datasheet.

Matrix Lie groups provide a language for describing motion in such fields as robotics, computer vision, and graphics. When using these tools, we are often faced with turning infinite-series expressions into more compact finite series (e.g., the Euler-Rodriques formula), which can sometimes be onerous. In this paper, we identify some useful integral forms in matrix Lie group expressions that offer a more streamlined pathway for computing compact analytic results. Moreover, we present some recursive structures in these integral forms that show many of these expressions are interrelated. Key to our approach is that we are able to apply the minimal polynomial for a Lie algebra quite early in the process to keep expressions compact throughout the derivations. With the series approach, the minimal polynomial is usually applied at the end, making it hard to recognize common analytic expressions in the result. We show that our integral method can reproduce several series-derived results from the literature.

Most autonomous vehicles rely on accurate and efficient localization, which is achieved by comparing live sensor data to a preexisting map, to navigate their environment. Balancing the accuracy of localization with computational efficiency remains a significant challenge, as high-accuracy methods often come with higher computational costs. In this paper, we present two ways of improving lidar localization efficiency and study their impact on performance. First, we integrate a lightweight Doppler-based odometry method into a topometric localization pipeline and compare its performance against an iterative closest point (ICP)-based method. We highlight the trade-offs between these approaches: the Doppler estimator offers faster, lightweight updates, while ICP provides higher accuracy at the cost of increased computational load. Second, by controlling the frequency of localization updates and leveraging odometry estimates between them, we demonstrate that accurate localization can be maintained while optimizing for computational efficiency using either odometry method. Our experimental results show that localizing every 10 lidar frames strikes a favourable balance, achieving a localization accuracy below 0.05 meters in translation and below 0.1 degrees in orientation while reducing computational effort by over 30% in an ICP-based pipeline. We quantify the trade-off of accuracy to computational effort using over 100 kilometers of real-world driving data in different on-road environments.

Continuous-time batch state estimation using Gaussian processes is an efficient approach to estimate the trajectories of robots over time. In the past, relatively simple physics-motivated priors have been considered for such approaches, using assumptions such as constant velocity or acceleration. This paper presents an approach to incorporating exogenous control inputs, such as velocity or acceleration commands, into the continuous Gaussian process state estimation framework. It is shown that this approach generalizes across different domains in robotics, making it applicable to both the estimation of continuous-time trajectories for mobile robots and the estimation of quasi-static continuum-robot shapes. Results show that incorporating control inputs leads to more informed priors, potentially requiring less measurements and estimation nodes to obtain accurate estimates. This makes the approach particularly useful in situations in which limited sensing is available. For example, in a mobile robot localization experiment with sparse landmark distance measurements and frequent odometry control inputs, our approach provides accurate trajectory estimates with root-mean-square errors around 3-4 cm and 4-5 degrees, even with time intervals up to five seconds between discrete estimation nodes, which significantly reduces computation time.

Treating inertial measurement unit (IMU) measurements as inputs to a motion model and then preintegrating these measurements have almost become a de facto standard in many robotics applications. However, this approach has a few shortcomings. First, it conflates the IMU measurement noise with the underlying process noise. Second, it is unclear how the state will be propagated in the case of IMU measurement dropout. Third, it does not lend itself well to dealing with multiple high-rate sensors such as a lidar and an IMU or multiple asynchronous IMUs. In this paper, we compare treating an IMU as an input to a motion model against treating it as a measurement of the state in a continuous-time state estimation framework. We methodically compare the performance of these two approaches on a 1D simulation and show that they perform identically, assuming that each method’s hyperparameters have been tuned on a training set. We also provide results for our continuous-time lidar-inertial odometry in simulation and on the Newer College Dataset. In simulation, our approach exceeds the performance of an imu-as-input baseline during highly aggressive motion. On the Newer College Dataset, we demonstrate state-of-the art results. These results show that continuous-time techniques and the treatment of the IMU as a measurement of the state are promising areas of further research. Code for our lidar-inertial odometry can be found at: https://github.com/utiasASRL/steam_icp .

How can a robot safely navigate around people with complex motion patterns? Deep Reinforcement Learning (DRL) in simulation holds some promise, but much prior work relies on simulators that fail to capture the nuances of real human motion. Thus, we propose Deep Residual Model Predictive Control (DR-MPC) to enable robots to quickly and safely perform DRL from real-world crowd navigation data. By blending MPC with model-free DRL, DR-MPC overcomes the DRL challenges of large data requirements and unsafe initial behavior. DR-MPC is initialized with MPC-based path tracking, and gradually learns to interact more effectively with humans. To further accelerate learning, a safety component estimates out-of-distribution states to guide the robot away from likely collisions. In simulation, we show that DR-MPC substantially outperforms prior work, including traditional DRL and residual DRL models. Hardware experiments show our approach successfully enables a robot to navigate a variety of crowded situations with few errors using less than 4 hours of training data (video: https://youtu.be/GUZlGBk60uY , code: https://github.com/James-R-Han/DR-MPC ).

Accurate, efficient, and robust state estimation is more important than ever in robotics as the variety of platforms and complexity of tasks continue to grow. Historically, discrete-time filters and smoothers have been the dominant approach, in which the estimated variables are states at discrete sample times. The paradigm of continuous-time state estimation proposes an alternative strategy by estimating variables that express the state as a continuous function of time, which can be evaluated at any query time. Not only can this benefit downstream tasks such as planning and control, but it also significantly increases estimator performance and flexibility, as well as reduces sensor preprocessing and interfacing complexity. Despite this, continuous-time methods remain underutilized, potentially because they are less well-known within robotics. To remedy this, this work presents a unifying formulation of these methods and the most exhaustive literature review to date, systematically categorizing prior work by methodology, application, state variables, historical context, and theoretical contribution to the field. By surveying splines and Gaussian processes together and contextualizing works from other research domains, this work identifies and analyzes open problems in continuous-time state estimation and suggests new research directions.

How can a robot safely navigate around people exhibiting complex motion patterns? Reinforcement Learning (RL) or Deep RL (DRL) in simulation holds some promise, although much prior work relies on simulators that fail to precisely capture the nuances of real human motion. To address this gap, we propose Deep Residual Model Predictive Control (DR-MPC), a method to enable robots to quickly and safely perform DRL from real-world crowd navigation data. By blending MPC with model-free DRL, DR-MPC overcomes the traditional DRL challenges of large data requirements and unsafe initial behavior. DR-MPC is initialized with MPC-based path tracking, and gradually learns to interact more effectively with humans. To further accelerate learning, a safety component estimates when the robot encounters out-of-distribution states and guides it away from likely collisions. In simulation, we show that DR-MPC substantially outperforms prior work, including traditional DRL and residual DRL models. Real-world experiments show our approach successfully enables a robot to navigate a variety of crowded situations with few errors using less than 4 hours of training data.

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.