應用於即時定位及姿態估測之電磁追蹤系統開發

Abstract

本論文開發即時電磁追蹤系統。磁場產生器由五個激勵線圈構成，以不同頻率的正弦電流同時驅動，於空間中產生不同方向的時變磁場。系統配置兩種磁場感測器，其一為單軸感應線圈，量測感應電動勢，其二為穿隧磁阻感測器模組，由三個正交排列的穿隧磁阻感測器組成，量測三軸磁通量密度。兩者訊號皆經由快速傅立葉分析擷取各頻率分量，並透過逆向模型估測磁場感測器的位置及姿態。 正向模型方面，感應線圈以高斯–勒讓得積分計算磁向量勢與磁通量，並以少量代表線圈與最佳化權重近似完整線圈的磁通量及相應的感應電動勢。穿隧磁阻感測器模組則採用必歐–沙伐定律，同樣結合高斯–勒讓得積分進行計算。兩種磁場感測器形式的正向模型皆以商用有限元素軟體驗證其正確性。此外，激勵線圈間的互感效應會影響追蹤效果，為此建立了激勵線圈互感模型。藉由量測每個線圈在各頻率的實際電流分量，以進行互感補償，提升模型準確性。 逆向模型結合深度神經網路與萊文伯格–馬夸特算法。將磁場感測器所量測的訊號輸入至預先完成訓練的深度神經網路中，並且將此估測結果作為萊文伯格–馬夸特算法的初始值，進一步獲得更精確的定位資訊。在連續追蹤過程中，則是將當前的追蹤結果作為下一次萊文伯格–馬夸特算法定位的初始值。基於抗噪能力評估，實驗選擇穿隧磁阻感測器模組作為磁場感測器以進行追蹤。 實驗先以單一激勵線圈驗證磁場感測器於平移及旋轉下之正向模型可行性，接著同時激勵兩個激勵線圈，納入線圈間的互感影響，並以實驗結果驗證互感補償的正確性。所建即時電磁追蹤系統的量測範圍為200mm×200mm×150mm，位置誤差落在1.7mm內，姿態誤差落在4.5°內，更新率為10Hz。

This thesis develops a real-time electromagnetic (EM) tracking system. The field generator comprises five excitation coils driven simultaneously with sinusoidal currents at distinct frequencies, producing time-varying magnetic fields in different spatial directions. The system adopts two types of magnetic sensors, namely a single-axis sensing coil for measuring the induced electromotive force (EMF) and a tunnel magnetoresistance (TMR) sensor module composed of three orthogonally arranged TMR sensors for measuring triaxial magnetic flux density. For both sensors, the acquired signals are processed using a fast Fourier transform (FFT) to extract the frequency-domain components, and an inverse model is employed to estimate the position and orientation of the magnetic sensor. For the forward model, the sensing coil is modeled by computing the magnetic vector potential and magnetic flux using Gauss–Legendre quadrature, while a small set of representative loops with optimized weights approximates a complete multi-turn coil to accurately reproduce the magnetic flux and the induced EMF. The TMR sensor module is modeled using the Biot–Savart law, also evaluated with Gauss–Legendre quadrature. The forward models of both sensor types are validated using commercial finite element analysis (FEA) software. Since mutual coupling among excitation coils can degrade tracking performance, a mutual inductance model is established. The harmonic current components in each excitation coil are measured and used to compensate for mutual coupling, thereby improving model accuracy. The inverse model combines the Levenberg–Marquardt (LM) algorithm with a deep neural network (DNN). Sensor measurements are first provided to a pre-trained DNN, and the estimate of the DNN initializes the LM algorithm to refine the pose estimation. During continuous tracking, the pose estimated at the current frame is used to initialize the LM algorithm for the next frame. Based on evaluations of noise robustness, the TMR sensor module is selected as the magnetic sensor in experiments. Experiments first validate the forward models by translating and rotating the magnetic sensor while driving a single excitation coil. Subsequently, two excitation coils are driven simultaneously to induce mutual coupling, and the effectiveness of the compensation scheme is validated experimentally. The developed real-time EM tracking system achieves a measurement volume of 200mm×200mm×150mm, a position error within 1.7mm, an orientation error within 4.5°, and an update rate of 10Hz.