Abstract-When a mobile agent does not known its position perfectly, incorporating the predicted uncertainty of future position estimates into the planning process can lead to substantially better motion performance. However, planning in the space of probabilistic position estimates, or belief space, can incur substantial computational cost. In this paper, we show that planning in belief space can be done efficiently for linear Gaussian systems by using a factored form of the covariance matrix. This factored form allows several prediction and measurement steps to be combined into a single linear transfer function, leading to very efficient posterior belief prediction during planning. We give a belief-space variant of the Probabilistic Roadmap algorithm called the Belief Roadmap (BRM) and show that the BRM can compute plans substantially faster than conventional belief space planning. We conclude with performance results for an agent using ultra-wide bandwidth (UWB) radio beacons to localize and show that we can efficiently generate plans that avoid failures due to loss of accurate position estimation.

This video highlights our system that enables a Micro Aerial Vehicle (MAV) to autonomously explore and map unstructured and unknown GPS-denied environments. While mapping and exploration solutions are now well-established for ground vehicles, air vehicles face unique challenges which have hindered the development of similar capabilities. Although there has been recent progress toward sensing, control, and navigation techniques for GPS-denied flight, there have been few demonstrations of stable, goal-directed flight in real-world environments. Our system leverages a multi-level sensing and control hierarchy that matches the computational complexity of the component algorithms with the real-time needs of a MAV to achieve autonomy in unconstrained environments.

This paper presents our solution for enabling a quadrotor helicopter to autonomously navigate unstructured and unknown indoor environments. We compare two sensor suites, specifically a laser rangefinder and a stereo camera. Laser and camera sensors are both well-suited for recovering the helicopter's relative motion and velocity. Because they use different cues from the environment, each sensor has its own set of advantages and limitations that are complimentary to the other sensor. Our eventual goal is to integrate both sensors on-board a single helicopter platform, leading to the development of an autonomous helicopter system that is robust to generic indoor environmental conditions. In this paper, we present results in this direction, describing the key components for autonomous navigation using either of the two sensors separately.

RGB-D cameras provide both color images and per-pixel depth estimates. The richness of this data and the recent development of low-cost sensors have combined to present an attractive opportunity for mobile robotics research. In this paper, we describe a system for visual odometry and mapping using an RGB-D camera, and its application to autonomous flight. By leveraging results from recent stateof-the-art algorithms and hardware, our system enables 3D flight in cluttered environments using only onboard sensor data. All computation and sensing required for local position control are performed onboard the vehicle, reducing the dependence on unreliable wireless links. However, even with accurate 3D sensing and position estimation, some parts of the environment have more perceptual structure than others, leading to state estimates that vary in accuracy across the environment. If the vehicle plans a path without regard to how well it can localize itself along that path, it runs the risk of becoming lost or worse. We show how the Belief Roadmap (BRM) algorithm (Prentice and Roy, 2009), a belief space extension of the Probabilistic Roadmap algorithm, can be used to plan vehicle trajectories that incorporate the sensing model of the RGB-D camera. We evaluate the effectiveness of our system for controlling a quadrotor micro air vehicle, demonstrate its use for constructing detailed 3D maps of an indoor environment, and discuss its limitations.Abraham Bachrach and Samuel Prentice contributed equally to this work.

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