#include #include #include #include #include #include "footPDR.h" #include "ekfPDR.h" #include "ukfPDR.h" #define ZUPT_threshold 0.81 #define SIGMA 0.01 #define SIGMA_V 0.01 #define PI 3.14159265f #define RUN 1 #define STAND 0 extern void sen_step_to_host(uint8_t, uint16_t); //当地的重力加速度 float g = 9.8179995f; float dt = 0.01f; float P[81], acc_n[3]; float Temporary_array1[9], Temporary_array2[9]; float K[27], P_prev[81], delta_x[9]; float C[9], C_prev[9]; float vel_n[3], pos_n[3]; float last_pos_n[3]; float pos_offset[3]; int frame_index = 0; int stand_num = 0; float gyr_norm_window[10]; float gyr_extreme[6]; float gyr_mean[3]; float num_peak; float acc_mean[3]; float gyrBias[3]; float last_gyr[3]; float last_acc[3]; float last_vel_n[3]; float accSum; float accSize; int press_data[10]; int ZUPT_STATUS; int press_index; int time_zupt; //last_stage:0 为 走路状态; //last_stage:1 为 静止状态 int last_stage; uint8_t step_count; uint16_t step_distance; int step_time = 0; //UKF参数 int UKF_L = 4; float UKF_alpha = 0.01f; float UKF_beta = 2.0f; float UKF_kappa = 0.0f; float gamma; float wm[9]; float wc[9]; float UKF_Q[4]; float UKF_P[4][4]; int UKF_iter; float mag_prev[3]; float deltaC[9]; float UKF_C[9]; float UKF_roll; float UKF_pitch; float UKF_yaw; float EKF_roll; float EKF_pitch; float EKF_yaw; int canUKF = 0; int stand_zupt_count = 0; //重置磁航向,计算双脚的磁航向,以确定身体的正朝向 float magSum_xyz[3]; float accSum_xyz[3]; float calHeading(float mag[3], float acc[3]) { float hSqrt; float eSqrt; float h[3]; //东向 h[0] = mag[1] * acc[2] - mag[2] * acc[1]; h[1] = mag[2] * acc[0] - mag[0] * acc[2]; h[2] = mag[0] * acc[1] - mag[1] * acc[0]; hSqrt = 1/sqrt(h[0] * h[0] + h[1] * h[1] + h[2] * h[2]); for(int i = 0; i < 3; i++) { h[i] *= hSqrt; } float e[3]; //北向 e[0] = acc[1] * h[2] - acc[2] * h[1]; e[1] = acc[2] * h[0] - acc[0] * h[2]; e[2] = acc[0] * h[1] - acc[1] * h[0]; eSqrt = 1/sqrt(e[0] * e[0] + e[1] * e[1] + e[2] * e[2]); for(int i = 0; i < 3; i++) { e[i] *= eSqrt; } return atan2(-h[1], e[1]); } void resetAttbyMag(float *C, float acc[3], float mag[3]) { float pitch = asin(-acc[0]); float roll = atan2(acc[1], acc[2]); float pitch_sin = sin(pitch); float pitch_cos = cos(pitch); float roll_sin = sin(roll); float roll_cos = cos(roll); float mag_heading; C[0] = pitch_cos; C[1] = pitch_sin * roll_sin; C[2] = pitch_sin * roll_cos; C[3] = 0.0; C[4] = roll_cos; C[5] = -roll_sin; mag_heading = atan2(C[4] * mag[1] + C[5] * mag[2], C[0] * mag[0] + C[1] * mag[1] + C[2] * mag[2]); float yaw_sin = sin(mag_heading); float yaw_cos = cos(mag_heading); C[0] = pitch_cos * yaw_cos; C[1] = pitch_sin * roll_sin * yaw_cos - roll_cos * yaw_sin; C[2] = pitch_sin * roll_cos * yaw_cos + roll_sin * yaw_sin; C[3] = pitch_cos * yaw_sin; C[4] = pitch_sin * roll_sin * yaw_sin + roll_cos * yaw_cos; C[5] = pitch_sin * roll_cos * yaw_sin - roll_sin * yaw_cos; C[6] = acc[0]; C[7] = acc[1]; C[8] = acc[2]; } void cal_step_data(void) { static int step_count_sum = 0; step_count = 1; step_count_sum += step_count; float step_length = sqrt((last_pos_n[0] - pos_n[0])*(last_pos_n[0] - pos_n[0]) + (last_pos_n[1] - pos_n[1])*(last_pos_n[1] - pos_n[1])); if (step_length > 5.0f) { step_length = 1.2f; } step_distance = (uint16_t)(step_length * 100.0f); //sen_step_to_host(step_count, step_distance); } uint8_t get_step_count(void) { return step_count; } uint16_t get_step_length(void) { return step_distance; } void Initialize(float *gyr, float *acc) { frame_index = 1; stand_num = 0; accSize = 1.0f; accSum = 0.0f; ZUPT_STATUS = 0; memset(last_pos_n, 0, 3 * sizeof(float)); memset(pos_offset, 0, 3 * sizeof(float)); memset(gyr_norm_window, 0, 10 * sizeof(float)); memset(P, 0, 81 * sizeof(float)); memset(acc_n, 0, 3 * sizeof(float)); memset(vel_n, 0, 3 * sizeof(float)); memset(pos_n, 0, 3 * sizeof(float)); memset(Temporary_array1, 0, 9 * sizeof(float)); memset(Temporary_array2, 0, 9 * sizeof(float)); memset(K, 0, 27 * sizeof(float)); memset(P_prev, 0, 81 * sizeof(float)); memset(delta_x, 0, 9 * sizeof(float)); memset(C, 0, 9 * sizeof(float)); memset(Temporary_array1, 0, 9 * sizeof(float)); memset(Temporary_array2, 0, 9 * sizeof(float)); memset(press_data, 0, 10 * sizeof(int)); init_attitude_matrix(C, acc, g); memcpy(C_prev, C, 9 * sizeof(float)); } void attitude_matrix_update(float *C, float *Temporary_array1, float *Temporary_array2, float *gyr, float dt) { Temporary_array1[0] = 2.0f; Temporary_array1[1] = dt * gyr[2]; Temporary_array1[2] = -dt * gyr[1]; Temporary_array1[3] = -dt * gyr[2]; Temporary_array1[4] = 2.0f; Temporary_array1[5] = dt * gyr[0]; Temporary_array1[6] = dt * gyr[1]; Temporary_array1[7] = -dt * gyr[0]; Temporary_array1[8] = 2.0f; invert3x3(Temporary_array1, Temporary_array2); memset(Temporary_array1, 0, 9 * sizeof(float)); Temporary_array1[0] = 2 * C[0] + C[1] * dt * gyr[2] - C[2] * dt * gyr[1]; Temporary_array1[1] = 2 * C[1] - C[0] * dt * gyr[2] + C[2] * dt * gyr[0]; Temporary_array1[2] = 2 * C[2] + C[0] * dt * gyr[1] - C[1] * dt * gyr[0]; Temporary_array1[3] = 2 * C[3] + C[4] * dt * gyr[2] - C[5] * dt * gyr[1]; Temporary_array1[4] = 2 * C[4] - C[3] * dt * gyr[2] + C[5] * dt * gyr[0]; Temporary_array1[5] = 2 * C[5] + C[3] * dt * gyr[1] - C[4] * dt * gyr[0]; Temporary_array1[6] = 2 * C[6] + C[7] * dt * gyr[2] - C[8] * dt * gyr[1]; Temporary_array1[7] = 2 * C[7] - C[6] * dt * gyr[2] + C[8] * dt * gyr[0]; Temporary_array1[8] = 2 * C[8] + C[6] * dt * gyr[1] - C[7] * dt * gyr[0]; multiply3x3(Temporary_array1, Temporary_array2, C); } float max_window_val(float *window, int window_size) { float val = window[0]; for (int i = 0; i < window_size; i++) { if (window[i] > val) val = window[i]; } return val; } int max_window_int(int *window, int window_size) { int val = window[0]; for (int i = 0; i < window_size; i++) { if (window[i] > val) val = window[i]; } return val; } float min_window_val(float *window, int window_size) { float val = window[0]; for (int i = 0; i < window_size; i++) { if (window[i] < val) val = window[i]; } return val; } int min_window_int(int *window, int window_size) { int val = window[0]; for (int i = 0; i < window_size; i++) { if (window[i] < val) val = window[i]; } return val; } //press_tren 函数功能:提供走路过程中上升沿,下降沿 //1 为上升 2 为 下降 0为不需要得状态 int press_trend(int index, int *window, int window_size) { int i; int max_val = window[(index - 1) % window_size]; int max_index = index; int min_val = max_val; int min_index = max_index; for (i = 1; i < window_size + 1; i++) { if (max_val < window[(index - i) % window_size]) { max_index = index - i + 1; max_val = window[(index - i) % window_size]; } if (min_val > window[(index - i) % window_size]) { min_index = index - i + 1; min_val = window[(index - i) % window_size]; } } if (max_index > min_index && max_val > min_val + 50000) { return 1; } if (max_index < min_index && max_val > min_val + 50000) { return 2; } return 0; } void dcm2angle(float *dcm, float *roll, float *pitch, float *yaw) { *yaw = atan2(dcm[3], dcm[0]); *pitch = asin(-dcm[6]); *roll = atan2(dcm[7], dcm[8]); } void quat2angleTest(float qin[4], float *roll, float *pitch, float *yaw) { //float r11 = qin[0] * qin[0] + qin[1] * qin[1] - qin[2] * qin[2] - qin[3] * qin[3]; float r11 = 2.0f * (qin[1] * qin[2] + qin[0] * qin[3]); //float r21 = 2.0f * (qin[1] * qin[2] - qin[0] * qin[3]); float r12 = qin[0] * qin[0] + qin[1] * qin[1] - qin[2] * qin[2] - qin[3] * qin[3]; float r21 = -2.0f * (qin[1] * qin[3] - qin[0] * qin[2]); float r31 = 2.0f * (qin[2] * qin[3] + qin[0] * qin[1]); float r32 = qin[0] * qin[0] - qin[1] * qin[1] - qin[2] * qin[2] + qin[3] * qin[3]; if (r21 < -0.999999999f) r21 = -1.0f; else if (r21 > 0.999999999f) r21 = 1.0f; *roll = atan2(r11, r12); *pitch = asin(r21); *yaw = atan2(r31, r32); } void dcm2angleTest(float C[9], short att[3]) { float yaw, pitch, roll; pitch = asin(-C[6]); if(C[6] > 0.999999f || C[6] < -0.999999f) { //当俯仰角为90度的时候,则假设翻滚角为0度 yaw = atan2(-C[1], C[4]); roll = 0.0f; } else { yaw = atan2(C[3], C[0]); roll = atan2(C[7], C[8]); } att[0] = (short)(yaw * 10000.f); //yaw att[1] = (short)(pitch * 10000.f); //pitch att[2] = (short)(roll * 10000.f); //roll } void quat2dcm(float *qin, float *dcm) { float qin_norm = 1 / sqrt(qin[0] * qin[0] + qin[1] * qin[1] + qin[2] * qin[2] + qin[3] * qin[3]); for (int i = 0; i < 4; i++) qin[i] *= qin_norm; dcm[0] = qin[0] * qin[0] + qin[1] * qin[1] - qin[2] * qin[2] - qin[3] * qin[3]; dcm[1] = 2.0f * (qin[1] * qin[2] + qin[0] * qin[3]); dcm[2] = 2.0f * (qin[1] * qin[3] - qin[0] * qin[2]); dcm[3] = 2.0f * (qin[1] * qin[2] - qin[0] * qin[3]); dcm[4] = qin[0] * qin[0] - qin[1] * qin[1] + qin[2] * qin[2] - qin[3] * qin[3]; dcm[5] = 2.0f * (qin[2] * qin[3] + qin[0] * qin[1]); dcm[6] = 2.0f * (qin[1] * qin[3] + qin[0] * qin[2]); dcm[7] = 2.0f * (qin[2] * qin[3] - qin[0] * qin[1]); dcm[8] = qin[0] * qin[0] - qin[1] * qin[1] - qin[2] * qin[2] + qin[3] * qin[3]; } void multiply3x3T(float *a, float *b, float* dst) { dst[0] = a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; dst[1] = a[0] * b[3] + a[1] * b[4] + a[2] * b[5]; dst[2] = a[0] * b[6] + a[1] * b[7] + a[2] * b[8]; dst[3] = a[3] * b[0] + a[4] * b[1] + a[5] * b[2]; dst[4] = a[3] * b[3] + a[4] * b[4] + a[5] * b[5]; dst[5] = a[3] * b[6] + a[4] * b[7] + a[5] * b[8]; dst[6] = a[6] * b[0] + a[7] * b[1] + a[8] * b[2]; dst[7] = a[6] * b[3] + a[7] * b[4] + a[8] * b[5]; dst[8] = a[6] * b[6] + a[7] * b[7] + a[8] * b[8]; } void deltaAttMatrix(float C_prev[9], float C_now[9], float deltaC[9]) { //detaC = C_prev'* C; deltaC[0] = C_now[0] * C_prev[0] + C_now[3] * C_prev[3] + C_now[6] * C_prev[6]; deltaC[1] = C_now[1] * C_prev[0] + C_now[4] * C_prev[3] + C_now[7] * C_prev[6]; deltaC[2] = C_now[2] * C_prev[0] + C_now[5] * C_prev[3] + C_now[8] * C_prev[6]; deltaC[3] = C_now[0] * C_prev[1] + C_now[3] * C_prev[4] + C_now[6] * C_prev[7]; deltaC[4] = C_now[1] * C_prev[1] + C_now[4] * C_prev[4] + C_now[7] * C_prev[7]; deltaC[5] = C_now[2] * C_prev[1] + C_now[5] * C_prev[4] + C_now[8] * C_prev[7]; deltaC[6] = C_now[0] * C_prev[2] + C_now[3] * C_prev[5] + C_now[6] * C_prev[8]; deltaC[7] = C_now[1] * C_prev[2] + C_now[4] * C_prev[5] + C_now[7] * C_prev[8]; deltaC[8] = C_now[2] * C_prev[2] + C_now[5] * C_prev[5] + C_now[8] * C_prev[8]; } void resetUKF(float *UKF_Q, float UKF_P[4][4], float *mag_prev, float *mag, float *UKF_C, float *C) { memset(UKF_Q, 0, 4 * sizeof(float)); UKF_Q[0] = 1.0f; memcpy(mag_prev, mag, 3 * sizeof(float)); memcpy(UKF_C, C, 9 * sizeof(float)); for (int i = 0; i < 4; i++) for (int j = 0; j < 4; j++) { UKF_P[i][j] = 0.0f; } for (int i = 0; i < 4; i++) { UKF_P[i][i] = 0.0000001f; } } //利用陀螺仪的双极端盘判断是否在稳定的范围 int isStandCon(float gyr_extreme[6]) { if(gyr_extreme[1] - gyr_extreme[0] < 0.008f && gyr_extreme[3] - gyr_extreme[2] < 0.008f && gyr_extreme[5] - gyr_extreme[4] < 0.008f) { return 1; } return 0; } unsigned char footPDR(int num, float *gyr, float *acc, float *mag ,int press, int16_t* pos_res, int16_t* att, int16_t* zupt) { unsigned char movement_e = 0; for (int i = 0; i < 3; i++) { accSum_xyz[i] += acc[i]; magSum_xyz[i] += mag[i]; gyr[i] *= (PI / 180); acc[i] *= g; } if (num_peak == 0) { for (int i = 0; i < 3; i++) { gyr_extreme[2 * i] = gyr[i]; gyr_extreme[2 * i + 1] = gyr[i]; } } for (int i = 0; i < 3; i++) { if (gyr[i] < gyr_extreme[2 * i]) { gyr_extreme[2 * i] = gyr[i]; } if (gyr[i] > gyr_extreme[2 * i + 1]) { gyr_extreme[2 * i + 1] = gyr[i]; } } accSum += sqrt(acc[0] * acc[0] + acc[1] * acc[1] + acc[2] * acc[2]); for (int i = 0; i < 3; i++) { gyr_mean[i] += gyr[i]; } num_peak++; //在线估计陀螺仪的零偏, 6050的零偏偏大 if (num_peak == 500) { if (isStandCon(gyr_extreme)) { float accSqrt = 1/sqrt(accSum_xyz[0] * accSum_xyz[0] + accSum_xyz[1] * accSum_xyz[1] + accSum_xyz[2] * accSum_xyz[2]); float magSqrt = 1/sqrt(magSum_xyz[0] * magSum_xyz[0] + magSum_xyz[1] * magSum_xyz[1] + magSum_xyz[2] * magSum_xyz[2]); for(int i = 0; i < 3; i++) { gyrBias[i] = gyr_mean[i] * 0.002f; accSum_xyz[i] *= accSqrt; magSum_xyz[i] *= magSqrt; } resetAttbyMag(C, accSum_xyz, magSum_xyz); resetUKF(UKF_Q, UKF_P, mag_prev, magSum_xyz, UKF_C, C); memset(P, 0, 81 * sizeof(float)); canUKF = 1; gpio_mt_run(50); } num_peak = 0; accSum = 0.0f; memset(gyr_mean, 0, 3 * sizeof(float)); memset(accSum_xyz, 0, 3 * sizeof(float)); memset(magSum_xyz, 0, 3 * sizeof(float)); } gyr[0] -= gyrBias[0]; gyr[1] -= gyrBias[1]; gyr[2] -= gyrBias[2]; float gyr_norm_xyz = sqrt(gyr[0] * gyr[0] + gyr[1] * gyr[1] + gyr[2] * gyr[2]); //需要一个滑动窗口来判断脚步是否在地上 frame_index++; //下面为惯导解算 if (num == 1 || frame_index < 0) { Initialize(gyr, acc); UKF_para(UKF_L, UKF_alpha, UKF_beta, UKF_kappa, &gamma, wm, wc); return movement_e; } //惯导解算: 姿态矩阵更新 attitude_matrix_update(C, Temporary_array1, Temporary_array2, gyr, dt); //惯导解算: 将IMU坐标系的加速度转换到“导航坐标系”下 multiply3x1(C, acc, acc_n); //惯导解算: 更新IMU速度 vel_n[0] = vel_n[0] + acc_n[0] * dt; vel_n[1] = vel_n[1] + acc_n[1] * dt; vel_n[2] = vel_n[2] + (acc_n[2] - g) * dt; //惯导解算: 更新IMU位置 pos_n[0] = pos_n[0] + vel_n[0] * dt; pos_n[1] = pos_n[1] + vel_n[1] * dt; pos_n[2] = pos_n[2] + vel_n[2] * dt; //ekf步骤: 状态协方差矩阵预测更新 //P = F*P*F' + Q; State_covariance_matrix_update(P, acc_n, dt); int window_index = (frame_index - 1) % 10; float gyr_norm_xz = sqrt(gyr[0] * gyr[0] + gyr[1] * gyr[1] + gyr[2] * gyr[2]); gyr_norm_window[window_index] = gyr_norm_xz; press_data[window_index] = press; //当press_trend函数返回是1,判断为踩地上 // 返回2 的时候,判断为离地 // 返回0 的时候,需要保持状态 int press_trend_val = press_trend(frame_index, press_data, 10); if (press_trend_val == 1) { ZUPT_STATUS = 1; } else if (press_trend_val == 2) { ZUPT_STATUS = 2; } //RUN_ZUPT mean detect on floor when running int RUN_ZUPT = 0; if ((frame_index > 10 && ZUPT_STATUS == 1)) RUN_ZUPT = 1; //STAND_ZUPT mean detect on floor when no any moving int STAND_ZUPT = 0; if ((frame_index > 15 && gyr_norm_window[window_index] < 0.35f && fabs(min_window_val(gyr_norm_window, 10) - max_window_val(gyr_norm_window, 10)) < 0.1f)) STAND_ZUPT = 1; //zupt if ((STAND_ZUPT || RUN_ZUPT)) { //计算一步的距离及步数+1 //做一个计算时间时间,防止非正常走路的情况出来 if (last_stage == 2 && frame_index - step_time > 30) { cal_step_data(); step_time = frame_index; } stand_num = stand_num + 1; time_zupt++; //ekf步骤: 计算卡尔曼滤波增益 //K = P*H'/(H*P*H' + R); Kalfman_gain(P, Temporary_array1, Temporary_array2, K); //ekf步骤: 观测误差更新 //delta_x = K * [vel_n(:,i);]; multiply9x3(K, vel_n, delta_x); //ekf步骤: 状态协方差矩阵观测更新 State_covariance_matrix_corr(P, P_prev, K); //这里先从设置 delta_x(3) = atan2(C(2,1),C(1,1)); //意味着每一步的参考方向是IMU X轴方向 // delta_x[2] = atan2(C[3], C[0]); // theta = -1.7801 + atan2(C[3], C[0]); // theta = 0.0f; //delta_x[2] = 0.0f; //修正姿态矩阵 Att_matrix_corr(C, C_prev, Temporary_array1, Temporary_array2, delta_x); //修正位置 pos_n_corr(pos_n, delta_x); //修正速度 vel_n_corr(vel_n, delta_x); last_pos_n[0] = pos_n[0]; last_pos_n[1] = pos_n[1]; last_pos_n[2] = pos_n[2]; last_stage = 1; *zupt = 1; } else { stand_num = 0; *zupt = 0; } //融合磁力计数据 // float mag_norm = sqrt(mag[0] * mag[0] + mag[1] * mag[1] + mag[2] * mag[2]); if(STAND_ZUPT) { stand_zupt_count ++; } else { stand_zupt_count = 0; } if(stand_zupt_count == 100 &&(mag_norm < 1.2f && mag_norm > 0.8f)) { mag[0] /= mag_norm; mag[1] /= mag_norm; mag[2] /= mag_norm; resetUKF(UKF_Q, UKF_P, mag_prev, mag, UKF_C, C); memset(P, 0, 81 * sizeof(float)); stand_zupt_count = 0; } if (canUKF && (mag_norm < 1.2f && mag_norm > 0.8f)) { mag[0] /= mag_norm; mag[1] /= mag_norm; mag[2] /= mag_norm; float magEst[3]; deltaAttMatrix(UKF_C, C, deltaC); multiply3x1(deltaC, mag, magEst); UKF_quat(UKF_Q, UKF_P, gyr, mag_prev, magEst, gamma, wm, wc, UKF_L, dt); //dcm=C_tmp * quat2dcm(X') * C_tmp' ; float dcm[9]; quat2dcm(UKF_Q, dcm); multiply3x3(UKF_C, dcm, deltaC); multiply3x3T(deltaC, UKF_C, dcm); dcm2angle(dcm, &EKF_roll, &EKF_pitch, &EKF_yaw); //float ukf_norm = 1 / sqrt(UKF_Q[0] * UKF_Q[0] + UKF_Q[1] * UKF_Q[1] + UKF_Q[2] * UKF_Q[2] + UKF_Q[3] * UKF_Q[3]); //UKF_Q[0] *= ukf_norm; //UKF_Q[1] *= ukf_norm; //UKF_Q[2] *= ukf_norm; //UKF_Q[3] *= ukf_norm; //quat2angle(UKF_Q, UKF_yaw, UKF_pitch, UKF_roll); Kalfman_gain_angle(P, Temporary_array1, Temporary_array2, K); State_covariance_matrix_corr_angle(P, P_prev, K); float angleErr[3]; angleErr[0] = 0.1f*( EKF_roll); angleErr[1] = 0.1f*( EKF_pitch); angleErr[2] = 0.1f*( EKF_yaw); multiply9x3(K, angleErr, delta_x); Att_matrix_corr(C, C_prev, Temporary_array1, Temporary_array2, delta_x); //修正位置 pos_n_corr(pos_n, delta_x); //修正速度 vel_n_corr(vel_n, delta_x); } //状态协方差矩阵保持正交性,以防出现退化 State_covariance_matrix_orthogonalization(P); memcpy(last_vel_n, vel_n, 3 * sizeof(float)); pos_offset[0] = pos_n[0] - last_pos_n[0]; pos_offset[1] = pos_n[1] - last_pos_n[1]; pos_offset[2] = pos_n[2] - last_pos_n[2]; dcm2angleTest(C, att); //航向角,俯仰角, 翻滚角(z y x) // att[0] = (short)(atan2(C[3], C[0]) * 10000.f); //yaw // att[1] = (short)(asin(-C[6]) * 10000.f); //pitch // att[2] = (short)(atan2(C[7], C[8]) * 10000.f); //roll // att[0] = (short)(1 ); //yaw // att[1] = (short)(2 ); //pitch // att[2] = (short)(3 ); //roll pos_res[0] = (short) (pos_offset[0] * 100.0f); pos_res[1] = (short) (pos_offset[1] * 100.0f); pos_res[2] = (short) (pos_offset[2] * 100.0f); if ((pos_res[0] * pos_res[0] + pos_res[1] * pos_res[1] + pos_res[2] * pos_res[2]) > 10) { last_stage = 2; } return movement_e; }