Nathan Michael

Kshitij Goel, Nathan Michael, Wennie Tabib

This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and adaptive methods have been proposed to address the challenge of balancing model fidelity with size. Instead, state-of-the-art mapping approaches require tuning parameters for specific use cases, but do not generalize across diverse environments. To address this gap, we utilize a self-organizing principle from information-theoretic learning to automatically adapt the complexity of the GMM model based on the relevant information in the sensor data. The approach is evaluated against existing point cloud modeling techniques on real-world data with varying degrees of scene complexity.

Micah Corah, Nathan Michael

In multi-robot multi-target tracking, robots coordinate to monitor groups of targets moving about an environment. We approach planning for such scenarios by formulating a receding-horizon, multi-robot sensing problem with a mutual information objective. Such problems are NP-Hard in general. Yet, our objective is submodular which enables certain greedy planners to guarantee constant-factor suboptimality. However, these greedy planners require robots to plan their actions in sequence, one robot at a time, so planning time is at least proportional to the number of robots. Solving these problems becomes intractable for large teams, even for distributed implementations. Our prior work proposed a distributed planner (RSP) which reduces this number of sequential steps to a constant, even for large numbers of robots, by allowing robots to plan in parallel while ignoring some of each others' decisions. Although that analysis is not applicable to target tracking, we prove a similar guarantee, that RSP planning approaches performance guarantees for fully sequential planners, by employing a novel bound which takes advantage of the independence of target motions to quantify effective redundancy between robots' observations and actions. Further, we present analysis that explicitly accounts for features of practical implementations including approximations to the objective and anytime planning. Simulation results -- available via open source release -- for target tracking with ranging sensors demonstrate that our planners consistently approach the performance of sequential planning (in terms of position uncertainty) given only 2--8 planning steps and for as many as 96 robots with a 24x reduction in the number of sequential steps in planning. Thus, this work makes planning for multi-robot target tracking tractable at much larger scales than before, for practical planners and general tracking problems.

Alexander Spitzer, Nathan Michael

This paper enhances the feedback linearization controller for multirotors with a learned acceleration error model and a thrust input delay mitigation model. Feedback linearization controllers are theoretically appealing but their performance suffers on real systems, where the true system does not match the known system model. We take a step in reducing these robustness issues by learning an acceleration error model, applying this model in the position controller, and further propagating it forward to the attitude controller. We show how this approach improves performance over the standard feedback linearization controller in the presence of unmodeled dynamics and repeatable external disturbances in both simulation and hardware experiments. We also show that our thrust control input delay model improves the step response on hardware systems.

Micah Corah, Nathan Michael

Volumetric objectives for exploration and perception tasks seek to capture a sense of value (or reward) for hypothetical observations at one or more camera views for robots operating in unknown environments. For example, a volumetric objective may reward robots proportionally to the expected volume of unknown space to be observed. We identify connections between existing information-theoretic and coverage objectives in terms of expected coverage, particularly that mutual information without noise is a special case of expected coverage. Likewise, we provide the first comparison, of which we are aware, between information-based approximations and coverage objectives for exploration, and we find, perhaps surprisingly, that coverage objectives can significantly outperform information-based objectives in practice. Additionally, the analysis for information and coverage objectives demonstrates that Randomized Sequential Partitions -- a method for efficient distributed sensor planning -- applies for both classes of objectives, and we provide simulation results in a variety of environments for as many as 32 robots.

Kshitij Goel, Wennie Tabib, Nathan Michael

This paper develops a communication-efficient distributed mapping approach for rapid exploration of a cave by a multi-robot team. Subsurface planetary exploration is an unsolved problem challenged by communication, power, and compute constraints. Prior works have addressed the problems of rapid exploration and leveraging multiple systems to increase exploration rate; however, communication considerations have been left largely unaddressed. This paper bridges this gap in the state of the art by developing distributed perceptual modeling that enables high-fidelity mapping while remaining amenable to low-bandwidth communication channels. The approach yields significant gains in exploration rate for multi-robot teams as compared to state-of-the-art approaches. The work is evaluated through simulation studies and hardware experiments in a wild cave in West Virginia.

Alexander Spitzer, Nathan Michael

We analyze and experimentally compare various rotational error metrics for use in quadrotor controllers. Traditional quadrotor attitude controllers have used Euler angles or the full rotation to compute an attitude error and scale that to compute a control response. Recently, several works have shown that prioritizing quadrotor tilt, or thrust vector error, in the attitude controller leads to improved position control, especially in situations with large yaw error. We provide a catalog of proposed rotational metrics, place them into the same framework, and show that we can independently reason about and design the magnitude of the response and the direction of the response. Existing approaches mainly fall into two categories: (1) metrics that induce a response in the shortest direction to correct the full rotation error and (2) metrics that combine a response in the shortest direction to correct tilt error with the shortest direction to correct yaw error. We show experimental results to highlight the salient differences between the rotational error metrics. See https://alspitz.github.io/roterrormetrics.html for an interactive simulation visualizing the experiments performed.

Kumar Shaurya Shankar, Nathan Michael

Traditional dense volumetric representations for robotic mapping make simplifying assumptions about sensor noise characteristics due to computational constraints. We present a framework that, unlike conventional occupancy grid maps, explicitly models the sensor ray formation for a depth sensor via a Markov Random Field and performs loopy belief propagation to infer the marginal probability of occupancy at each voxel in a map. By explicitly reasoning about occlusions our approach models the correlations between adjacent voxels in the map. Further, by incorporating learnt sensor noise characteristics we perform accurate inference even with noisy sensor data without ad-hoc definitions of sensor uncertainty. We propose a new metric for evaluating probabilistic volumetric maps and demonstrate the higher fidelity of our approach on simulated as well as real-world datasets.

Wennie Tabib, Kshitij Goel, John Yao et al.

This paper presents a method for cave surveying in total darkness using an autonomous aerial vehicle equipped with a depth camera for mapping, downward-facing camera for state estimation, and forward and downward lights. Traditional methods of cave surveying are labor-intensive and dangerous due to the risk of hypothermia when collecting data over extended periods of time in cold and damp environments, the risk of injury when operating in darkness in rocky or muddy environments, and the potential structural instability of the subterranean environment. Although these dangers can be mitigated by deploying robots to map dangerous passages and voids, real-time feedback is often needed to operate robots safely and efficiently. Few state-of-the-art, high-resolution perceptual modeling techniques attempt to reduce their high bandwidth requirements to work well with low bandwidth communication channels. To bridge this gap in the state of the art, this work compactly represents sensor observations as Gaussian mixture models and maintains a local occupancy grid map for a motion planner that greedily maximizes an information-theoretic objective function. The approach accommodates both limited field of view depth cameras and larger field of view LiDAR sensors and is extensively evaluated in long duration simulations on an embedded PC. An aerial system is leveraged to demonstrate the repeatability of the approach in a flight arena as well as the effects of communication dropouts. Finally, the system is deployed in Laurel Caverns, a commercially owned and operated cave in southwestern Pennsylvania, USA, and a wild cave in West Virginia, USA.

Alexander Spitzer, Nathan Michael

We present a control strategy that applies inverse dynamics to a learned acceleration error model for accurate multirotor control input generation. This allows us to retain accurate trajectory and control input generation despite the presence of exogenous disturbances and modeling errors. Although accurate control input generation is traditionally possible when combined with parameter learning-based techniques, we propose a method that can do so while solving the relatively easier non-parametric model learning problem. We show that our technique is able to compensate for a larger class of model disturbances than traditional techniques can and we show reduced tracking error while following trajectories demanding accelerations of more than 7 m/s^2 in multirotor simulation and hardware experiments.

Alex Spitzer, Xuning Yang, John Yao et al.

We present a multirotor architecture capable of aggressive autonomous flight and collision-free teleoperation in unstructured, GPS-denied environments. The proposed system enables aggressive and safe autonomous flight around clutter by integrating recent advancements in visual-inertial state estimation and teleoperation. Our teleoperation framework maps user inputs onto smooth and dynamically feasible motion primitives. Collision-free trajectories are ensured by querying a locally consistent map that is incrementally constructed from forward-facing depth observations. Our system enables a non-expert operator to safely navigate a multirotor around obstacles at speeds of 10 m/s. We achieve autonomous flights at speeds exceeding 12 m/s and accelerations exceeding 12 m/s^2 in a series of outdoor field experiments that validate our approach.

Bo Fu, Kumar Shaurya Shankar, Nathan Michael

State-of-the-art forward facing monocular visual-inertial odometry algorithms are often brittle in practice, especially whilst dealing with initialisation and motion in directions that render the state unobservable. In such cases having a reliable complementary odometry algorithm enables robust and resilient flight. Using the common local planarity assumption, we present a fast, dense, and direct frame-to-frame visual-inertial odometry algorithm for downward facing cameras that minimises a joint cost function involving a homography based photometric cost and an IMU regularisation term. Via extensive evaluation in a variety of scenarios we demonstrate superior performance than existing state-of-the-art downward facing odometry algorithms for Micro Aerial Vehicles (MAVs).

Michael S. Lee, Matthew Hanczor, Jiyang Chu et al.

Radiation detection has largely been a manual inspection process with point sensors such as Geiger-Muller counters and scintillation spectrometers to date. While their observations of source proximity prove useful, they lack the directional information necessary for efficient source localization and characterization in cluttered environments with multiple radiation sources. The recent commercialization of Compton gamma cameras provides directional information to the broader radiation detection community for the first time. This paper presents the integration of a Compton gamma camera with a self-localizing ground robot for accurate 3D radiation mapping. Using the position and orientation of the robot, radiation images from the gamma camera are accumulated over a traversed path in a shared frame of reference to construct a consistent voxel grid-based radiation map. The peaks of the map at pre-specified energy windows are selected as the source location estimates, which are compared to the ground truth source locations. The proposed approach localizes multiple sources to within an average of 0.2 m in two 5 x 4 m^2 and 14 x 6 m^2 laboratory environments.

Aditya Dhawale, Kumar Shaurya Shankar, Nathan Michael

Size, weight, and power constrained platforms impose constraints on computational resources that introduce unique challenges in implementing localization algorithms. We present a framework to perform fast localization on such platforms enabled by the compressive capabilities of Gaussian Mixture Model representations of point cloud data. Given raw structural data from a depth sensor and pitch and roll estimates from an on-board attitude reference system, a multi-hypothesis particle filter localizes the vehicle by exploiting the likelihood of the data originating from the mixture model. We demonstrate analysis of this likelihood in the vicinity of the ground truth pose and detail its utilization in a particle filter-based vehicle localization strategy, and later present results of real-time implementations on a desktop system and an off-the-shelf embedded platform that outperform localization results from running a state-of-the-art algorithm on the same environment.

Nancy Amato, Charles Anderson, Gregory Chirikjian et al.

Proceedings of the 1st International Workshop on Robot Learning and Planning (RLP 2016)