I'm trying to apply IK to my human skeleton's arm, where the shoulder position is fixed, and only the arm is moving.
The FK of the arm looks like this
(x,y,z) = Root_T * Shoulder_T * Shoulder_Rx(q_0) * Shoulder_Ry(q_1) *
Shoulder_Rz(q_2) * Elbow_T * Elbow_Rx(q_3) * Hand_T * Hand_Rx(q_4) * Position
This is my IK solver function
//Q_desired is a 5*1 Vector whose entries are initialized as 0.0
//TargetP is where I want the end effector to be
void BoneRig::solveIK(glm::vec3& targetP, Eigen::VectorXf& Q_desired) {
//Basic setups
float error = 10.0f;
glm::vec3 errorP;
Eigen::VectorXf deltaQ(5);
glm::vec3 endEffector = glm::vec3(0.0f,0.0f,0.0f);
Eigen::MatrixXf J(3,5);
Eigen::MatrixXf J_plus(5,3);
float deltaTime = 0.1;
int limit = 1000;
int limitCounter = 0;
while(error > 0.01){
//gets the current endEffector location and stores it in endEffector
getEndEffectorP(endEffector);
errorP = targetP - endEffector;
Eigen::VectorXf deltaX(3);
deltaX << (errorP * deltaTime).x, (errorP * deltaTime).y, (errorP * deltaTime).z;
getJacobian(J, targetP);
J_plus = J.transpose();
deltaQ = J_plus * deltaX;
Q_desired += deltaQ;
setOrientation(Q_desired);
error = glm::length(errorP);
if(limitCounter>= limit){
std::cout << "You could not solve this"<<std::endl;
break;
}
}
}
I think the problem is in setOrientation(Q_desired); function. Q_desired = Q_desired + deltaQ updates the DOF angles in every loop, so I update the rotation matrices of each joints accordingly. Here is the setOrientation(Q_desired) function.
//Joints[15] is the Shoulder joint, Joints[16] is the Elbow joint.
//Joints[17] is the Hand joint
void BoneRig::setOrientation(const Eigen::VectorXf& ceta_d){
glm::mat4 temp = glm::mat4(1.0f);
Joints[15].setR(glm::rotate(temp,ceta_d(0),glm::vec3(1.0f,0.0f,0.0f)));
Joints[15].setR(glm::rotate(Joints[15].returnR(),ceta_d(1),glm::vec3(0.0f,1.0f,0.0f)));
Joints[15].setR(glm::rotate(Joints[15].returnR(),ceta_d(2),glm::vec3(0.0f,0.0f,1.0f)));
temp = glm::mat4(1.0f);
Joints[16].setR(glm::rotate(temp,ceta_d(3),glm::vec3(1.0f, 0.0f, 0.0f)));
temp = glm::mat4(1.0f);
Joints[17].setR(glm::rotate(temp,ceta_d(4),glm::vec3(1.0f, 0.0f, 0.0f)));
return;
}
I was curious if applying the angle rotations should be done in those rotation axis (Should it be the global axis, and not the local axis?) I didn't post the getJacobian() method because I think it's right, but I will if there's no flaw in this code. Any help would be appreciated. Thanks in advance!
EDIT This is how I get the Jacobian matrix for the arm. Note that only the shoulder is the ball and socket joint and the rest are just revolute joints based on the local x-axis.
void BoneRig::getJacobian(Eigen::MatrixXf& J, glm::vec3& targetWorld){
glm::vec4 xAxis = glm::vec4(1.0f,0.0f,0.0f,0.0f);
glm::vec4 yAxis = glm::vec4(0.0f,1.0f,0.0f,0.0f);
glm::vec4 zAxis = glm::vec4(0.0f,0.0f,1.0f,0.0f);
glm::mat4 temp = Joints[0].returnT() * Joints[0].returnR() * Joints[11].returnT() * Joints[11].returnR() * Joints[14].returnT() * Joints[14].returnR() * Joints[15].returnT() * Joints[15].returnR();
glm::vec3 worldXAxis = glm::vec3(temp * xAxis);
glm::vec3 worldYAxis = glm::vec3(temp * yAxis);
glm::vec3 worldZAxis = glm::vec3(temp * zAxis);
glm::vec3 worldPos = glm::vec3(temp * glm::vec4(0.0f,0.0f,0.0f, 1.0f));
glm::vec3 p = targetWorld - worldPos;
glm::vec3 upperPart = glm::cross(worldXAxis,p);
J(0,0) = upperPart.x;
J(1,0) = upperPart.y;
J(2,0) = upperPart.z;
upperPart = glm::cross(worldYAxis,p);
J(0,1) = upperPart.x;
J(1,1) = upperPart.y;
J(2,1) = upperPart.z;
upperPart = glm::cross(worldZAxis,p);
J(0,2) = upperPart.x;
J(1,2) = upperPart.y;
J(2,2) = upperPart.z;
temp = temp * Joints[16].returnT() * Joints[16].returnR();
worldXAxis = glm::vec3(temp * xAxis);
worldPos = glm::vec3(temp * glm::vec4(0.0f,0.0f,0.0f, 1.0f));
p = targetWorld - worldPos;
upperPart = glm::cross(worldXAxis,p);
J(0,3) = upperPart.x;
J(1,3) = upperPart.y;
J(2,3) = upperPart.z;
temp = temp * Joints[17].returnT() * Joints[17].returnR();
worldXAxis = glm::vec3(temp * xAxis);
worldPos = glm::vec3(temp * glm::vec4(0.0f,0.0f,0.0f, 1.0f));
p = targetWorld - worldPos;
upperPart = glm::cross(worldXAxis,p);
J(0,4) = upperPart.x;
J(1,4) = upperPart.y;
J(2,4) = upperPart.z;
}
I used this equation for each column of the Jacobian Matrix. The axis should be calculated in global coordinates, so that's what I did in the code.
