Specialized Algorithm for Navigation of a Micro Hopping Air Vehicle Using Only Inertial Sensors

The need for accurate and reliable navigation techniques for micro air vehicles plays an important part in enabling autonomous operation. Traditional navigation systems typically rely on periodic GPS updates and provide little benefit when operating indoors or in other similarly shielded environments. Moreover, direct integration of the onboard inertial measurement unit (IMU) data stream often results in substantial drift errors yielding virtually unusable positional information. This paper presents a new strategy for obtaining an accurate navigation solution for the special case of a micro hopping air vehicle, beginning from some known location and heading, using only one triaxial accelerometer and one triaxial gyroscope. Utilising the unique dynamics of the hopping vehicle, a piece-wise navigation solution is constructed by selectively integrating the inertial data stream for only those short periods of time while the vehicle is airborne. Inter-hop data post-processing and sensor bias recalibration are also used to further improve estimation accuracy. To assess the performance of the proposed algorithm, a series of tests were conducted in which the estimated vehicle position following a sequence of 10 consecutive hops was compared with measurements from an optical motion-capture system. On average, the final estimated vehicle position was within 0.70 m or just over 6% from its actual location based on a total traveled distance of approximately 11 m. Nomenclature ~a = vehicle linear acceleration vector ax, ay, az = body frame components of the vehicle mass center acceleration BAi, BGi = ith component of the accelerometer and gyroscope bias vector C j Ai, C j Gi = cross-axis sensitivity of accelerometer and gyroscope i th axis with respect to the jth axis F = linearized system matrix g = gravitational acceleration H = linearized measurement matrix I = identity matrix K = Kalman gain matrix NAi, NGi = ith component of accelerometer and gyroscope noise vector P, Q, R = error, process noise, and measurement noise covariance matrices p, q, r = angular velocity components in body reference frame ~ra→b = position vector extending from generic point a to another point b Costello DS-11-1315 1 SA, SG = scaling matrices of accelerometer and gyroscope SAi, SGi = scale factor for ith axis of accelerometer and gyroscope TIB = transformation matrix from body to inertial reference frame TSB = transformation matrix from body to sensor reference frame t = time u, v, w = body frame components of vehicle translation velocity ~v, ~w = measurement and process noise vectors x, y, z = inertial position components of vehicle mass center ~x = system state vector ~y = system output vector ~z = sensor measurement vector ~α = vehicle angular acceleration vector ~δA = accelerometer misposition vector φ, θ, ψ = vehicle Euler roll, pitch, and yaw angles ~ω = vehicle angular velocity vector Subscript B = body reference frame I = inertial reference frame S = sensor reference frame Superscript ∗ = raw sensor value