MEMSセンサを用いた 小型INS/GPS航法装置 の開発 56367 成岡 優 指導教員: 土屋助教授 Thank you for your kind introduction, Mr. Chairman. My name is Masaru Naruoka, and I’m a graduated student of the university of Tokyo. Today, we will talk about “A Portable and Cost-effective Configuration of Strap-down INS/GPS for General-purpose Use”.

概要 背景: 小型、軽量、安価かつ高精度な航法装置の必要性 手法 評価: 精度はどれくらいか? 結論 2018/11/9 修士輪講会2006 背景: 小型、軽量、安価かつ高精度な航法装置の必要性 手法 評価: 精度はどれくらいか? 結論 This is the outline of my talk. First, as the background, we will talk about we need precise but small, light and inexpensive navigation system. And then, I’d like to propose my system as the method. Next, we will discuss about the evaluation of my system. As the evaluation, we check how precise my system is. Finally, I will summarize this talk. Let’s start with the background. 2018/11/9 修士輪講会2006

背景 (1/5) 高精度な航法データの必要性 多くのアプリケーションて精度よい航法情報(位置や速度、姿勢)が必要とされる 飛行機や宇宙機のナビゲーション 車や電車等の移動体の監視 ロボットやUAVの誘導制御 As I named this presentation “general-purpose use”, there are many applications for requiring precise navigation data. Here, the navigation data is basic state values like position, velocity and attitude of the target. In these applications, navigating aircrafts and spacecrafts of course are included. Other than that, for example, there are observing moving objects like cars, trains, controlling robots, UAVs, and so on. Then, we get one idea. Can we apply accumulated navigation technologies of aircrafts to these applications? 航空機で培われたナビゲーション技術を 汎用的に利用することはできないか? 2018/11/9 修士輪講会2006

背景 (2/5) 優れた航空機の航法技術の1つとしてINS/GPS 慣性航法装置 (INS) Global Positioning System (GPS) + 早い更新周期 but 誤差が蓄積 誤差が蓄積しない but 更新周期が低い As one of the navigation technologies of aircrafts, there is INS/GPS navigation system. This system is combined two navigation systems, INS and GPS. INS is Inertial navigation system and GPS is global positioning system. INS/GPS utilizes both benefit and compensate each other’s disadvantage. INS updates output frequently, but its precision degrades as time progresses. Meanwhile, the error of GPS output is canceled when time passes, but its update ratio is low. Then to combine INS and GPS, the INS/GPS update ratio is high and the error is canceled. 早い更新周期 and 誤差蓄積しない 2018/11/9 修士輪講会2006

背景 (3/5) INS/GPSの仕組み INS GPS 統合 INS/GPS 位置, 速度, 姿勢 慣性センサ 受信機 位置 衛星 加速度 運動の法則 三角測量 INS GPS 慣性センサ 受信機 加速度 角速度 位置 速度 姿勢 衛星 位置 速度 電波 This is the mechanism of INS/GPS. INS utilize the laws of motion. INS calculates position, velocity and attitude based on acceleration and angular speed obtained by inertial sensors. So, the performance of INS mainly depends on inertial sensors. On the other hand, GPS utilizes triangle surveying. GPS calculates its position and velocity by a receiver processing radio wave from GPS satellites. As the satellites are common, the performance of GPS is depend on the receiver. INS/GPS integrates both outputs, and calculates position, velocity and attitude as a whole system. 統合 INS/GPS 位置, 速度, 姿勢 2018/11/9 修士輪講会2006

背景 (4/5) 航空機 vs. 汎用 INS/GPS 航空機向け(既存) 汎用向け(近年開発中) 高精度? 超高精度 (誤差: <1m, <1deg) 高精度? Trade-Off 着目点 大きい(> 1000 cm3) 重い (> 1 kg) 小さい (< 1000 cm3) 軽い (< 1 kg) 飛行機、宇宙機のみ! However, there is rare case to use traditional INS/GPS devices for general-purpose use. This is because they are too big, heavy and expensive. They are intended for use on special targets such as aircrafts and spacecrafts that require their ultra precision. Then, recently the new INS/GPS devices have been developing for general-purpose use. They are small, light, and cost-effective at the expense of their precision. In other words, their 1st priority is size, weight and cost, and their 2nd priority is precision. However, in order to aim true general-purpose use, we must think precision is also important. This is the motivation of my study. 安価 (< 100万円) 高価 (> 100万円) 2018/11/9 修士輪講会2006

背景 (5/5) 研究目的 精度とその他スペックの間に存在するトレードオフを議論することは非常に重要である 本研究の目的 できる限り小さく、軽く、安価なINS/GPS装置を構成し その精度を正確に評価し、汎用的に使用可能か検討する Here we establish the goal of my study. 1. 2. 2018/11/9 修士輪講会2006

手法 (1/7) 構成機器 使用しない 使用する 高精度だが大きく重く高価な特殊部品 Ring laser gyro 軍用、特殊用GPS 小さく軽く安価な汎用部品 MEMS慣性センサ 民生用GPS Then we will move to the method to build my system. First, I will talk about the limitation for components that we use. The traditional INS/GPS devices are big, heavy and expensive because of dedicated components. For example, a ring laser gyro and a military-use GPS receiver. We don’t use such dedicated components. On the other hand, the developing INS/GPS uses small, light and inexpensive components, like MEMS sensors and a civil-use GPS receiver. We use them. 2018/11/9 修士輪講会2006

手法 (2/7) MEMSセンサと民生用GPS MEMS慣性センサ 民生用GPS受信機 電気回路と検出部を一体化 小さく(~1 cm2), 軽く(<1 g), 安価(<1万円) MEMS慣性センサを用いたINSは誤差が非常に早く溜まりやすい. 民生用GPS受信機 カーナビなどに使われている 小さく(~10 cm2), 軽く(<10g), 安価(~1万円) 比較的よい精度 (位置誤差: 10~20m) Let’s look closely MEMS sensors and a civil-use GPS receiver. A MEMS sensor utilize the MEMS technology, which integrates electronic circuit and sensing elements into one small package, and is small, light and inexpensive sensor. // Its size is about 1 cm^2, its weight is under 1 g and its cost is under $ 100. But it is noted that an INS device using MEMS sensors accumulates error very quickly. And, A civil-use GPS receiver is used mostly as car navigation system, and thank you for developed packaging technology and mass production, it is also small, light and inexpensive. // Its size is about 10 cm^2, its weight is under 10 g, and its cost is about $ 100. In addition, its precision is good. Its error is about 10 to 20 m in position. 2018/11/9 修士輪講会2006

手法 (3/7) INS/GPSアルゴリズム Strap-down構成 機械的なジンバルが必要ない extended Kalman filtering (EKF)による統合 Loose-coupling: 計算リソースの節約 クォータニオンの活用 MEMSセンサの大きな誤差を補償するための数学的に単純なモデル オイラー角で発生するような特異点を完全に除去 We chose the components of my INS/GPS system, and next is the algorithm. We select the strap-down configuration. It enables us to make the system small, light and low-cost, because it don’t need for any mechanical structure. And Extended Kalman filtering, EKF is used as integration method of my INS/GPS. This filtering utilize both INS and GPS maximally. We select the loose-coupling among various EKF integrations because it requires small calculation power relatively. These two are used broadly in the developing INS/GPS device. In addition to these, we actively use quaternion for modeling the system. This is because in order to compensate for large MEMS sensor error we require mathematically simple model. As the result, we can eliminate singular points and get linearized model for EKF to observe the norm unity condition of quaternion. Next, we look closely the algorithm with equations. 2018/11/9 修士輪講会2006

手法 (4/7) 式(1) : INS運動方程式 速度 (3[North, East, Down Speed] 状態量) Acceleration Gravity 位置 (4[Latitude, Longitude, Azimuth] + 1[Height] = 5 状態量) This is the equations of motion for my INS. We use quaternions for position and attitude. Latitude, longitude and azimuth are represented as one quaternion. And roll, pitch and heading are also represented as one quaternion. quaternion 姿勢 (4[Roll, Pitch, Heading] 状態量) Angular Speed 2018/11/9 修士輪講会2006

手法 (5/7) 式(2) : EKF向け線形化 大きさを維持したままのクォータニオンの線形化 INS運動方程式に以下の代入をすることでEKF用の線形化が完了する quaternion Next is the linearization for EKF. We can obtain linearized form for EKF by these substitutions to the equations of motion. Here, we use multiplicative form for quaternion linearization. normal linearization is performed by giving the Jacobian, that is, the additive form. However, this form of a quaternion yields the norm change. Therefore, we use the multiplicative form to keep the unity of quaternions. 大きさを維持したままのクォータニオンの線形化 Jacobian i.e. 足し算型 (4 状態量) 掛け算型 (3 状態量) 2018/11/9 修士輪講会2006

手法 (6/7) 式(3) : EKF EKF Time Update EKF Correct INSが時間更新するとき GPSから情報が得られたとき EKF Time Update EKF Correct quaternion These equations are used in EKF. When the equations of motion for INS are updated, the EKF time update is performed. When an output of GPS is obtained, the EKF correct is performed and state values of the INS is modified by EKF. 2018/11/9 修士輪講会2006

手法 (7/7) 全体図 Strap-down構成 MEMS 慣性センサ クォータニオンの利用 民生用GPS 2018/11/9 As the final slide of the method, I will summarize the proposed INS/GPS system. This figure shows the overall view of my system. My INS/GPS consists of MEMS inertial sensors and a civil-use GPS receiver with strap-down configuration. MEMS inertial sensors are calibrated. And, we use EKF for INS/GPS integration, and leverage quaternions for system modeling. 民生用GPS 2018/11/9 修士輪講会2006

評価 (1/11) 概要 プロトタイプ 精度評価試験 提案手法に基づいて作成 較正を行う プロトタイプと高精度な既存航法装置の比較 Next, we will move the evaluation of my system. This is the outline of the evaluation. We can divide the evaluation into two phases, prototyping and the test for precision. In the prototyping we make a prototype to check the size, weight, and cost of my system. Moreover, we calibrate the prototype. In the test, we compare the prototype with an existent precise navigation device on order to check the precision of my system. 2018/11/9 修士輪講会2006

評価 (2/11) プロトタイプ 大きさ: ~ 100 cm3 重さ: ~ 30 g 費用: ~ 3万円 小さく、軽く、安価である (構造部材ぬきで) First I will introduce the prototype. This picture is a look of the prototype. MEMS sensors and a civil-use GPS receiver are used. Without the structural element, the size of the prototype is under 100 cm^3, its weight is under 30 g and its cost is about $ 300. That is, the prototype shows my system is small, light, and low-cost. 小さく、軽く、安価である 2018/11/9 修士輪講会2006

評価 (3/11) プロトタイプ詳細 2018/11/9 修士輪講会2006 This is the detail of the prototype. The prototype consists of MEMS sensors, a civil-use GPS receiver, an analog-digital converter, and a USB interface to communicate with a PC. In this prototype, for ease, the calculation is performed by a PC. 2018/11/9 修士輪講会2006

容易に取り除ける誤差要因の中で最も効果が大きい 評価 (4/11) MEMS INSの較正 温度ドリフト 取付け誤差 rotating settling 容易に取り除ける誤差要因の中で最も効果が大きい Before we move the test, I will introduce the calibration that I performed. Developing INS with MEMS inertial sensors, we calibrate the temperature drift and the misalignment. This is because It is known that these two effect are main reasons of the INS error that can be removed easily. The temperature drift is measured by settling a sensor on a temperature-controlled bath. When a MEMS sensor has the drift, the result will be tilted. And, the misalignement is measured by using a rate table. When a MEMS gyro is misaligned, the result also be titled. 2018/11/9 修士輪講会2006

評価 (5/11) 較正結果 温度ドリフトと取付け誤差の測定結果 温度ドリフト 取付け誤差 傾いている 傾いている Y,Z X 温度 This is the result of the calibration. As you see, the temperature drift and the misalignment are recognized. 温度 真の角速度 (X軸) vs. vs. 検出加速度 (X-軸 加速度計) 検出角速度 (X, Y, Z-軸 ジャイロ) 2018/11/9 修士輪講会2006

評価 (6/11) 精度評価試験 GAIAとの比較 (2006/06) GAIA: JAXAによって開発された超高精度なINS/GPS装置、誤差は絶対位置で < 1m 同JAXA所有の実験用航空機 MuPAL-a内にプロトタイプとGAIAを設置 飛行し、両者の履歴を比較 Next, we will talk about the test for precision. In the test, GAIA is used as the comparative reference. GAIA is an ultra high-precision INS/GPS device developed by Japan Aerospace Exploration Agency, JAXA. Its precision is under 1 m in absolute position. The test is performed in flight of an experimental aircraft, MuPAL-alpha of JAXA. 2018/11/9 修士輪講会2006

評価 (7/11) 実景風景 GAIA MuPAL-a プロトタイプ 2018/11/9 修士輪講会2006 This is the scene of the test. This is GAIA, and MuPAL-alpha. The prototype and GAIA is fixed on MuPAL-alpha. MuPAL-a プロトタイプ 2018/11/9 修士輪講会2006

評価 (8/11) 試験結果 プロトタイプ: 赤 GAIA: 緑 位置 (3D) 速度 姿勢 GAIAとほぼ等しい 2018/11/9 This is the result of the flight test. You can recognize that the output of the prototype is nearly equal to the output of GAIA. Let’s look closely the result. 位置 (3D) 速度 姿勢 GAIAとほぼ等しい 2018/11/9 修士輪講会2006

評価 (9/11) 結果詳細 GAIAを基準としたときの プロトタイプの誤差の統計量 位置 < 10m 速度 < 2 deg This table shows the statistical summary of the error of the prototype by reference to GAIA. In consideration of the mean and the standard deviation, the precision is under 10m in position, under 2 degrees in roll and pitch, over 10 degrees in heading. < 2 deg 姿勢 > 10 deg 2018/11/9 修士輪講会2006

評価 (10/11) 試験結果のまとめと考察 誤差: < 10 m(位置), < 2 deg(ロール、ピッチ) 汎用的に使用するのに十分な精度と考えられる ヘディングが特に悪い (誤差: >10 deg) 運動の周波数モードの影響が考えられる ロールやピッチは比較的高い周波数の運動 (> 1Hz) 一方ヘディングは周波数の低い運動 (< 1 Hz) 除去が難しい周波数の低いノイズ成分、例えばゼロ点変動と重なってしまっている Here, I will summarize and discuss the result of the test. The error of the prototype is under 10 m in position and under 2 degrees in roll and pitch. Therefore, I think the precision of the proposed configuration is enough for general-purpose use. However the precision of heading is especially bad. It is over 10 degrees. I think this is because of frequency mode effect of the target dynamics. Roll and Pitch are comparatively high mode. Their frequency are over 1 Hz. In other hand, heading is low mode, whose frequency is under 1 Hz. And this mode overlaps with low mode noise that cannot remove easily, for example, zero-point change of sensors. 2018/11/9 修士輪講会2006

評価 (11/11) 較正の効果 較正あり 較正なし 較正の効果を確認できる 例 : ロール履歴 2018/11/9 修士輪講会2006 As the last slide of the evaluation, I will show you the effectiveness of calibration. Without calibration, the output is degraded too much. You can say that the calibration works well. 例 : ロール履歴 較正の効果を確認できる 2018/11/9 修士輪講会2006

結論 提案した手法とその結果 汎用的利用を目指した小さく、軽く、安価なINS/GPSを提案した MEMS慣性センサと民生用GPS受信機を構成機器とし、 Strap-down構成をとった アルゴリズムではEKFとQuaternionを利用した 温度ドリフトと取付け誤差を較正し、その効果を確認した 試験結果によると、汎用利用には十分な精度を有する、誤差は位置で10 m以内、ロールとピッチで2度以内であった Finally, I will summarize my presentation. My navigation system is as small, light and cost-effective as other developing INS/GPS devices for general-purpose use. The system is the strap-down INS/GPS configuration using MEMS sensors and a civil-use GPS receiver. And, the effect of the temperature drift and the misalignment is calibrated. The main algorithm of my system is EKF and the system model is described by using quaternions. Finally the test shows my system is precise enough for general-purpose use because its error is under 10 meters in position and under 2 degrees in roll and pitch. Thank you for you kind listening. Are there any questions? 2018/11/9 修士輪講会2006

今後の課題 低い周波数のノイズへの対応 時間-周波数解析 他の補強システムの利用 Waveletによる多重解像度解析 地磁気センサ 2018/11/9 修士輪講会2006