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This work presents a multiplicative extended Kalman filter (MEKF) for estimating the relative state of a multirotor vehicle operating in a GPS-denied environment. The filter fuses data from an inertial measurement unit and altimeter with relative-pose updates from a keyframe-based visual odometry or laser scan-matching algorithm. Because the global position and heading states of the vehicle are unobservable in the absence of global measurements such as GPS, the filter in this article estimates the state with respect to a local frame that is colocated with the odometry keyframe. As a result, the odometry update provides nearly direct measurements of the relative vehicle pose, making those states observable. Recent publications have rigorously documented the theoretical advantages of such an observable parameterization, including improved consistency, accuracy, and system robustness, and have demonstrated the effectiveness of such an approach during prolonged multirotor flight tests. This article complements this prior work by providing a complete, self-contained, tutorial derivation of the relative MEKF, which has been thoroughly motivated but only briefly described to date. This article presents several improvements and extensions to the filter while clearly defining all quaternion conventions and properties used, including several new useful properties relating to error quaternions and their Euler-angle decomposition. Finally, this article derives the filter both for traditional dynamics defined with respect to an inertial frame, and for robocentric dynamics defined with respect to the vehicle’s body frame, and provides insights into the subtle differences that arise between the two formulations.

Many current approaches for navigation of micro air vehicles (MAVs) in GPS-degraded environments use a globally-referenced state for estimation and control, even though this state is not observable when GPS is unavailable. By working with respect to a local reference frame, the relative navigation (RN) framework presented in this paper ensures that the state maintains observability and that the uncertainty remains bounded, consistent, and normally-distributed. RN further insulates flight-critical estimation and control processes from the large global updates common in GPSdegraded MAV flight. This paper provides a thorough description of the details needed to successfully implement the RN framework on a MAV. The practicality of RN is demonstrated in several long flight tests in unknown, GPS-denied and GPS-degraded environments. The relative front end is shown to produce low-drift estimates and smooth, stable control while leveraging off-the-shelf algorithms. The system runs in real time with onboard processing, fuses a variety of vision sensors, works indoors and outdoors, and does not require special tuning for particular sensors or environments. RN is also shown to produce globally-consistent, metric, and localized maps by incorporating loop closures and intermittent GPS measurements. This map is used to demonstrate autonomous completion of mission objectives. By subtly restructuring the estimation framework, RN promotes a paradigm shift that avoids many issues inherent in GPS-degraded navigation.

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While collision avoidance and flight stability are generally a micro air vehicle's (MAVs) highest priority, many map-based path planning algorithms focus on path optimality, often assuming a static, known environment. For many MAV applications a robust navigation solution requires responding quickly to obstacles in dynamic, tight environments with nonnegligible disturbances. This article first outlines the Reactive Obstacle Avoidance Plugin framework as a method for leveraging map-based algorithms while providing low-latency, high-bandwidth response to obstacles. Further, we propose and demonstrate the effectiveness of the Cushioned Extended-Periphery Avoidance (CEPA) algorithm. By representing recent laser scans in the current body-fixed polar coordinate frame, a 360 ○ lower-bound understanding of the environment is available. With this extended field of view, motion assumptions common in other reactive planners can be relaxed and emergency control effort can be applied in any direction. CEPA is validated in simulation and on hardware in a GPS-denied environment using strictly onboard computation and sensing.