内容

本教程主要讲解了一个3DOF的平面机器人在mujoco
中的模拟

xml模型文件的建立
怎么获取每个关节的位置和速度
怎么获取每个躯干的姿态（四元数表示，以及将其转成欧拉形式）
控制方法是通过设置重力在x方向上的0.1倍作为驱动机器人前行的动力,通知摆动脚前半段缩起，后半段再伸出

视频教程

MuJoCo Lec13

模型代码

因为是2D行走，所以base是有3个自由度的：

          <joint name="x" type="slide" pos="0 0 0.5" axis = "1 0 0" /><joint name="z" type="slide" pos="0 0 0.5" axis = "0 0 1" /><joint name="pin" type="hinge" pos="0 0 0.5" axis="0 -1 0" />

这里将base的关节直接就建在Leg上，有点不适合。
正常的情况下，base的自由度是独立于腿的，附在pelvis上，类似下面的的方法：

      <body name="pelvis" pos="0 0 0.355"> <inertial diaginertia="0.0006208 0.000533 0.0000389" mass="0.256" pos="0 0 0"/><!-- <joint type="free" limited='false'  damping="0" stiffness="0" armature="0" pos="0 0 0"/> --><joint type='slide' axis='1 0 0' limited='false'/><joint type='slide' axis='0 1 0' limited='false'/><joint type='slide' axis='0 0 1' limited='false'/><joint name="rotx" axis="1 0 0" type="hinge" limited="false" armature="0" damping="0"/><joint name="roty" axis="0 1 0" type="hinge" limited="false" armature="0" damping="0"/><joint name="rotz" axis="0 0 1" type="hinge" limited="false" armature="0" damping="0"/>

另外，还有一个比较奇怪的地方，Leg2居然是作为Leg1的子树，其实Leg1,Leg2应该是独立的分支
才对，这样后面做动力学推导时，才比较简单。

完整的模型代码

<mujoco><visual><headlight ambient="0.25 0.25 0.25"/></visual><option timestep="0.001" integrator="RK4" gravity="0 0 0"><flag sensornoise="disable" contact="enable" energy="enable"/></option><worldbody><geom type="plane" size="1000 5 0.1" rgba=".9 0 0 1"/><body name="leg1" pos="0 0 0.75" euler="0 0 0"><joint name="x" type="slide" pos="0 0 0.5" axis = "1 0 0" /><joint name="z" type="slide" pos="0 0 0.5" axis = "0 0 1" /><joint name="pin" type="hinge" pos="0 0 0.5" axis="0 -1 0" /><geom type="cylinder" size=".05 .5" rgba="0 .9 0 1" mass="1"/><body name="foot1" pos="0 0 -0.75"><joint name="knee1" type="slide" pos="0 0 0.25" axis = "0 0 -1" /><geom type="sphere" size=".05" rgba=".9 .9 0 1" mass="0.1"/></body><body name="leg2" pos="0 0.25 0" euler="0 0 0"><joint name="hip" type="hinge" pos="0 0 0.5" axis="0 -1 0" /><geom type="cylinder" size=".05 .5" rgba=".9 .9 .9 1" mass="1"/><body name="foot2" pos="0 0 -0.75"><joint name="knee2" type="slide" pos="0 0 0.25" axis = "0 0 -1" /><geom type="sphere" size=".05" rgba=".9 .9 0 1" mass="0.1"/></body></body></body></worldbody><!-- <equality><connect body1='pole' body2='world' anchor='0 0 0.5'/></equality> --><actuator><position name="pservo_hip" joint="hip" kp="4"/><velocity name="vservo_hip" joint="hip" kv="1"/><position name="pservo_knee1" joint="knee1" kp="1000"/><velocity name="vservo_knee1" joint="knee1" kv="100"/><position name="pservo_knee2" joint="knee2" kp="1000"/><velocity name="vservo_knee2" joint="knee2" kv="100"/></actuator></mujoco>

控制代码

main.c

#include <QCoreApplication>#include<stdbool.h>//for bool
//#include<unistd.h> //for usleep
//#include <math.h>#include "mujoco.h"
#include "glfw3.h"
#include "stdio.h"
#include "stdlib.h"
#include "string.h"#include "util.h"int fsm_hip;
int fsm_knee1;
int fsm_knee2;#define fsm_leg1_swing 0
#define fsm_leg2_swing 1#define fsm_knee1_stance 0
#define fsm_knee1_retract 1
#define fsm_knee2_stance 0
#define fsm_knee2_retract 1int step_no;//simulation end time
double simend = 60;//related to writing data to a file
FILE *fid;
int loop_index = 0;
const int data_frequency = 10; //frequency at which data is written to a file// char xmlpath[] = "../myproject/template_writeData/pendulum.xml";
// char datapath[] = "../myproject/template_writeData/data.csv";//Change the path <template_writeData>
//Change the xml file
char path[] = "H:/mujoco_learn/Code/biped/biped/";
char xmlfile[] = "biped.xml";char datafile[] = "data.csv";// MuJoCo data structures
mjModel *m = NULL;                  // MuJoCo model
mjData *d = NULL;                   // MuJoCo data
mjvCamera cam;                      // abstract camera
mjvOption opt;                      // visualization options
mjvScene scn;                       // abstract scene
mjrContext con;                     // custom GPU context// mouse interaction
bool button_left = false;
bool button_middle = false;
bool button_right =  false;
double lastx = 0;
double lasty = 0;// holders of one step history of time and position to calculate dertivatives
mjtNum position_history = 0;
mjtNum previous_time = 0;// controller related variables
float_t ctrl_update_freq = 100;
mjtNum last_update = 0.0;
mjtNum ctrl;// keyboard callback
void keyboard(GLFWwindow *window, int key, int scancode, int act, int mods)
{// backspace: reset simulationif (act == GLFW_PRESS && key == GLFW_KEY_BACKSPACE){mj_resetData(m, d);mj_forward(m, d);}
}// mouse button callback
void mouse_button(GLFWwindow *window, int button, int act, int mods)
{// update button statebutton_left = (glfwGetMouseButton(window, GLFW_MOUSE_BUTTON_LEFT) == GLFW_PRESS);button_middle = (glfwGetMouseButton(window, GLFW_MOUSE_BUTTON_MIDDLE) == GLFW_PRESS);button_right = (glfwGetMouseButton(window, GLFW_MOUSE_BUTTON_RIGHT) == GLFW_PRESS);// update mouse positionglfwGetCursorPos(window, &lastx, &lasty);
}// mouse move callback
void mouse_move(GLFWwindow *window, double xpos, double ypos)
{// no buttons down: nothing to doif (!button_left && !button_middle && !button_right)return;// compute mouse displacement, savedouble dx = xpos - lastx;double dy = ypos - lasty;lastx = xpos;lasty = ypos;// get current window sizeint width, height;glfwGetWindowSize(window, &width, &height);// get shift key statebool mod_shift = (glfwGetKey(window, GLFW_KEY_LEFT_SHIFT) == GLFW_PRESS ||glfwGetKey(window, GLFW_KEY_RIGHT_SHIFT) == GLFW_PRESS);// determine action based on mouse buttonmjtMouse action;if (button_right)action = mod_shift ? mjMOUSE_MOVE_H : mjMOUSE_MOVE_V;else if (button_left)action = mod_shift ? mjMOUSE_ROTATE_H : mjMOUSE_ROTATE_V;elseaction = mjMOUSE_ZOOM;// move cameramjv_moveCamera(m, action, dx / height, dy / height, &scn, &cam);
}// scroll callback
void scroll(GLFWwindow *window, double xoffset, double yoffset)
{// emulate vertical mouse motion = 5% of window heightmjv_moveCamera(m, mjMOUSE_ZOOM, 0, -0.05 * yoffset, &scn, &cam);
}//****************************
//This function is called once and is used to get the headers
void init_save_data()
{//write name of the variable here (header)fprintf(fid, "t, ");//Don't remove the newlinefprintf(fid, "\n");
}//***************************
//This function is called at a set frequency, put data here
void save_data(const mjModel *m, mjData *d)
{//data here should correspond to headers in init_save_data()//seperate data by a space %f followed by spacefprintf(fid, "%f ", d->time);//Don't remove the newlinefprintf(fid, "\n");
}/******************************/
void set_torque_control(const mjModel *m, int actuator_no, int flag)
{if (flag == 0)m->actuator_gainprm[10 * actuator_no + 0] = 0;elsem->actuator_gainprm[10 * actuator_no + 0] = 1;
}
/******************************//******************************/
void set_position_servo(const mjModel *m, int actuator_no, double kp)
{m->actuator_gainprm[10 * actuator_no + 0] = kp;m->actuator_biasprm[10 * actuator_no + 1] = -kp;
}
/******************************//******************************/
void set_velocity_servo(const mjModel *m, int actuator_no, double kv)
{m->actuator_gainprm[10 * actuator_no + 0] = kv;m->actuator_biasprm[10 * actuator_no + 2] = -kv;
}
/******************************///**************************
void init_controller(const mjModel *m, mjData *d)
{
//d->qpos[4] = 0.5;d->ctrl[0] = d->qpos[4];
//mj_forward(m,d);fsm_hip = fsm_leg2_swing;fsm_knee1 = fsm_knee1_stance;fsm_knee2 = fsm_knee2_stance;step_no = 0;}//**************************
void mycontroller(const mjModel *m, mjData *d)
{//write control hereint body_no;double quat0, quatx, quaty, quatz;double euler_x, euler_y, euler_z;double abs_leg1, abs_leg2;double z_foot1, z_foot2;double x = d->qpos[0]; double vx = d->qvel[0];double z = d->qpos[1]; double vz = d->qvel[1];double q1 = d->qpos[2]; double u1 = d->qvel[2];double l1 = d->qpos[3]; double l1dot = d->qvel[3];double q2 = d->qpos[4]; double u2 = d->qvel[4];double l2 = d->qpos[5]; double l2dot = d->qvel[5];//state estimationbody_no = 1;quat0 = d->xquat[4 * body_no]; quatx = d->xquat[4 * body_no + 1];quaty = d->xquat[4 * body_no + 2]; quatz = d->xquat[4 * body_no + 3];quat2euler(quat0, quatx, quaty, quatz, &euler_x, &euler_y, &euler_z);//printf("Body = %d; euler angles = %f %f %f \n",body_no,euler_x,euler_y,euler_z);abs_leg1 = -euler_y;body_no = 3;quat0 = d->xquat[4 * body_no]; quatx = d->xquat[4 * body_no + 1];quaty = d->xquat[4 * body_no + 2]; quatz = d->xquat[4 * body_no + 3];quat2euler(quat0, quatx, quaty, quatz, &euler_x, &euler_y, &euler_z);//printf("Body = %d; euler angles = %f %f %f \n",body_no,euler_x,euler_y,euler_z);abs_leg2 = -euler_y;//x = d->qpos[3*body_no]; y = d->qpos[3*body_no + 1];body_no = 2;z_foot1 = d->xpos[3 * body_no + 2];//printf("%f \n",z_foot1);body_no = 4;z_foot2 = d->xpos[3 * body_no + 2];//All transitions hereif (fsm_hip == fsm_leg2_swing && z_foot2 < 0.05 && abs_leg1 < 0){fsm_hip = fsm_leg1_swing;step_no += 1;printf("step_no = %d \n", step_no);}if (fsm_hip == fsm_leg1_swing && z_foot1 < 0.05 && abs_leg2 < 0){fsm_hip = fsm_leg2_swing;step_no += 1;printf("step_no = %d \n", step_no);}if (fsm_knee1 == fsm_knee1_stance && z_foot2 < 0.05 && abs_leg1 < 0){fsm_knee1 = fsm_knee1_retract;}if (fsm_knee1 == fsm_knee1_retract && abs_leg1 > 0.1){fsm_knee1 = fsm_knee1_stance;}if (fsm_knee2 == fsm_knee2_stance && z_foot1 < 0.05 && abs_leg2 < 0){fsm_knee2 = fsm_knee2_retract;}if (fsm_knee2 == fsm_knee2_retract && abs_leg2 > 0.1){fsm_knee2 = fsm_knee2_stance;}//All actions hereif (fsm_hip == fsm_leg1_swing){d->ctrl[0] = -0.5;}if (fsm_hip == fsm_leg2_swing){d->ctrl[0] = 0.5;}if (fsm_knee1 == fsm_knee1_stance){d->ctrl[2] = 0;}if (fsm_knee1 == fsm_knee1_retract){d->ctrl[2] = -0.25;}if (fsm_knee2 == fsm_knee2_stance){d->ctrl[4] = 0;}if (fsm_knee2 == fsm_knee2_retract){d->ctrl[4] = -0.25;}//write data here (dont change/dete this function call; instead write what you need to save in save_data)if (loop_index % data_frequency == 0){save_data(m, d);}loop_index = loop_index + 1;
}//************************
// main function
int main(int argc,   char **argv)
{QCoreApplication a(argc, argv);char xmlpath[100] = {};char datapath[100] = {};strcat(xmlpath, path);strcat(xmlpath, xmlfile);strcat(datapath, path);strcat(datapath, datafile);// load and compile modelchar error[1000] = "Could not load binary model";// check command-line argumentsif (argc < 2)m = mj_loadXML(xmlpath, 0, error, 1000);else if (strlen(argv[1]) > 4 && !strcmp(argv[1] + strlen(argv[1]) - 4, ".mjb"))m = mj_loadModel(argv[1], 0);elsem = mj_loadXML(argv[1], 0, error, 1000);if (!m)mju_error_s("Load model error: %s", error);// make datad = mj_makeData(m);// init GLFWif (!glfwInit())mju_error("Could not initialize GLFW");// create window, make OpenGL context current, request v-syncGLFWwindow *window = glfwCreateWindow(1244, 700, "Demo", NULL, NULL);glfwMakeContextCurrent(window);glfwSwapInterval(1);// initialize visualization data structuresmjv_defaultCamera(&cam);mjv_defaultOption(&opt);mjv_defaultScene(&scn);mjr_defaultContext(&con);mjv_makeScene(m, &scn, 2000);                // space for 2000 objectsmjr_makeContext(m, &con, mjFONTSCALE_150);   // model-specific context// install GLFW mouse and keyboard callbacksglfwSetKeyCallback(window, keyboard);glfwSetCursorPosCallback(window, mouse_move);glfwSetMouseButtonCallback(window, mouse_button);glfwSetScrollCallback(window, scroll);//double arr_view[] = {89.608063, -11.588379, 8, 0.000000, 0.000000, 2.000000}; //view the left side (for ll, lh, left_side)double arr_view[] = {120.893610, -15.810496, 8.000000, 0.000000, 0.000000, 2.000000};cam.azimuth = arr_view[0];cam.elevation = arr_view[1];cam.distance = arr_view[2];cam.lookat[0] = arr_view[3];cam.lookat[1] = arr_view[4];cam.lookat[2] = arr_view[5];// install control callbackmjcb_control = mycontroller;fid = fopen(datapath, "w");init_save_data();init_controller(m, d);double gamma = 0.1; //ramp slopedouble gravity = 9.81;m->opt.gravity[2] = -gravity * cos(gamma);m->opt.gravity[0] = gravity * sin(gamma);// use the first while condition if you want to simulate for a period.while (!glfwWindowShouldClose(window)){// advance interactive simulation for 1/60 sec//  Assuming MuJoCo can simulate faster than real-time, which it usually can,//  this loop will finish on time for the next frame to be rendered at 60 fps.//  Otherwise add a cpu timer and exit this loop when it is time to render.mjtNum simstart = d->time;while (d->time - simstart < 1.0 / 60.0){mj_step(m, d);}if (d->time >= simend){fclose(fid);break;}// get framebuffer viewportmjrRect viewport = {0, 0, 0, 0};glfwGetFramebufferSize(window, &viewport.width, &viewport.height);//opt.frame = mjFRAME_WORLD; //mjFRAME_BODY//opt.flags[mjVIS_COM]  = 1 ; //mjVIS_JOINT;opt.flags[mjVIS_JOINT]  = 1 ;// update scene and rendermjv_updateScene(m, d, &opt, NULL, &cam, mjCAT_ALL, &scn);mjr_render(viewport, &scn, &con);//int body = 2;//cam.lookat[0] = d->xpos[3*body+0];cam.lookat[0] = d->qpos[0];//printf("{%f, %f, %f, %f, %f, %f};\n",cam.azimuth,cam.elevation, cam.distance,cam.lookat[0],cam.lookat[1],cam.lookat[2]);// swap OpenGL buffers (blocking call due to v-sync)glfwSwapBuffers(window);// process pending GUI events, call GLFW callbacksglfwPollEvents();}// free visualization storagemjv_freeScene(&scn);mjr_freeContext(&con);// free MuJoCo model and data, deactivatemj_deleteData(d);mj_deleteModel(m);mj_deactivate();// terminate GLFW (crashes with Linux NVidia drivers)
#if defined(__APPLE__) || defined(_WIN32)glfwTerminate();
#endifreturn a.exec();
}

工具类：util.h

#ifndef UTIL_H
#define UTIL_Hvoid mat2euler(double dircos[3][3],double *a1,double *a2,double *a3)
{double th1, th2, th3, temp[10];if (((fabs(dircos[0][2]) - 1.) >= -1e-15)){th1 = atan2(dircos[2][1], dircos[1][1]);if ((dircos[0][2] > 0.)){temp[0] = 1.5707963267949;}else{temp[0] = -1.5707963267949;}th2 = temp[0];th3 = 0.;}else{th1 = atan2(-dircos[1][2], dircos[2][2]);th2 = asin(dircos[0][2]);th3 = atan2(-dircos[0][1], dircos[0][0]);}*a1 = th1;*a2 = th2;*a3 = th3;
}void mat2quat(double dircos[3][3],double *e4, //constdouble *e1, //qxdouble *e2, //qydouble *e3) //qz
{double tmp, tmp1, tmp2, tmp3, tmp4, temp[10];tmp = (dircos[0][0] + (dircos[1][1] + dircos[2][2]));if (((tmp >= dircos[0][0]) && ((tmp >= dircos[1][1]) && (tmp >= dircos[2][2])))){tmp1 = (dircos[2][1] - dircos[1][2]);tmp2 = (dircos[0][2] - dircos[2][0]);tmp3 = (dircos[1][0] - dircos[0][1]);tmp4 = (1. + tmp);}else{if (((dircos[0][0] >= dircos[1][1]) && (dircos[0][0] >= dircos[2][2]))){tmp1 = (1. - (tmp - (2.*dircos[0][0])));tmp2 = (dircos[0][1] + dircos[1][0]);tmp3 = (dircos[0][2] + dircos[2][0]);tmp4 = (dircos[2][1] - dircos[1][2]);}else{if ((dircos[1][1] >= dircos[2][2])){tmp1 = (dircos[0][1] + dircos[1][0]);tmp2 = (1. - (tmp - (2.*dircos[1][1])));tmp3 = (dircos[1][2] + dircos[2][1]);tmp4 = (dircos[0][2] - dircos[2][0]);}else{tmp1 = (dircos[0][2] + dircos[2][0]);tmp2 = (dircos[1][2] + dircos[2][1]);tmp3 = (1. - (tmp - (2.*dircos[2][2])));tmp4 = (dircos[1][0] - dircos[0][1]);}}}tmp = (1. / sqrt(((tmp1 * tmp1) + ((tmp2 * tmp2) + ((tmp3 * tmp3) + (tmp4 * tmp4))))));*e1 = (tmp * tmp1);*e2 = (tmp * tmp2);*e3 = (tmp * tmp3);*e4 = (tmp * tmp4);
}void euler2mat(double a1,double a2,double a3,double dircos[3][3])
{double cos1, cos2, cos3, sin1, sin2, sin3;cos1 = cos(a1);cos2 = cos(a2);cos3 = cos(a3);sin1 = sin(a1);sin2 = sin(a2);sin3 = sin(a3);dircos[0][0] = (cos2 * cos3);dircos[0][1] = -(cos2 * sin3);dircos[0][2] = sin2;dircos[1][0] = ((cos1 * sin3) + (sin1 * (cos3 * sin2)));dircos[1][1] = ((cos1 * cos3) - (sin1 * (sin2 * sin3)));dircos[1][2] = -(cos2 * sin1);dircos[2][0] = ((sin1 * sin3) - (cos1 * (cos3 * sin2)));dircos[2][1] = ((cos1 * (sin2 * sin3)) + (cos3 * sin1));dircos[2][2] = (cos1 * cos2);
}void quat2mat(double ie4, //constantdouble ie1, //qxdouble ie2, //qydouble ie3, //qzdouble dircos[3][3])
{double e1, e2, e3, e4, e11, e22, e33, e44, norm;e11 = ie1 * ie1;e22 = ie2 * ie2;e33 = ie3 * ie3;e44 = ie4 * ie4;norm = sqrt(e11 + e22 + e33 + e44);if (norm == 0.){e4 = 1.;norm = 1.;}else{e4 = ie4;}norm = 1. / norm;e1 = ie1 * norm;e2 = ie2 * norm;e3 = ie3 * norm;e4 = e4 * norm;e11 = e1 * e1;e22 = e2 * e2;e33 = e3 * e3;dircos[0][0] = 1. - (2.*(e22 + e33));dircos[0][1] = 2.*(e1 * e2 - e3 * e4);dircos[0][2] = 2.*(e1 * e3 + e2 * e4);dircos[1][0] = 2.*(e1 * e2 + e3 * e4);dircos[1][1] = 1. - (2.*(e11 + e33));dircos[1][2] = 2.*(e2 * e3 - e1 * e4);dircos[2][0] = 2.*(e1 * e3 - e2 * e4);dircos[2][1] = 2.*(e2 * e3 + e1 * e4);dircos[2][2] = 1. - (2.*(e11 + e22));
}void euler2quat(double a1, double a2, double a3, double *e4, double *e1, double *e2, double *e3)
{double dircos[3][3];double tmp1, tmp2, tmp3, tmp4;euler2mat(a1, a2, a3, dircos);mat2quat(dircos, &tmp4, &tmp1, &tmp2, &tmp3);*e4 = tmp4; //constant*e1 = tmp1;*e2 = tmp2;*e3 = tmp3;
}void quat2euler(double e4, double e1, double e2, double e3, double *a1, double *a2, double *a3)
{double dircos[3][3];double tmp1, tmp2, tmp3;quat2mat(e4, e1, e2, e3, dircos);mat2euler(dircos, &tmp1, &tmp2, &tmp3);*a1 = tmp1;*a2 = tmp2;*a3 = tmp3;
}#endif// UTIL_H

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