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RigidBody.h
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RigidBody.h
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#ifndef RIGIDBODY_H
#define RIGIDBODY_H
#include <Eigen/Eigen>
#include <CarPlanner/SE3.h>
#include <CarPlanner/CarPlannerCommon.h>
struct State {
float x; // position
float v; // velocity
};
struct Derivative {
float dx; // derivative of position: velocity
float dv; // derivative of velocity: acceleration
};
class RigidBody {
public:
RigidBody() {
m_vG << 0, 0, 9.81;
}
void Init(Eigen::Matrix3d inertia, double dMass) {
m_vI = inertia;
//the inverse of the inertia tensor
m_vII = m_vI.inverse();
m_dMass = dMass;
m_dTime = -1;
//reset everything
m_vV << 0, 0, 0;
m_vW = m_vPosition = m_vRotation = m_vW;
}
void RollBackMotion(double dT) {
m_vPosition -= (m_vV * dT);
m_vRotation += (m_vW * dT);
}
// the forces and moments applied are relative to body coordinates
void UpdateMotion(Eigen::Vector3d force, Eigen::Vector3d torque, double forceDt = -1, bool bIncludeGravity = true, bool bInBodyCoords = false) {
//if this is the first time the function is called, get a timestamp and exit
if (m_dTime == -1) {
m_dTime = Tic();
return;
}
Eigen::Matrix3d R = fusion::Cart2R(m_vW);
//if given in body coordinates, rotate them to suit
if (bInBodyCoords == true) {
force = R*force;
torque = R*torque;
}
//if gravity is to be included, we have to have it in body coordinates
if (bIncludeGravity == true) {
//add the rotated force to the total force acting on the body
force += R*m_vG;
}
//get the time elapsed since the last time this function was called
double dT = Toc(m_dTime);
m_dTime = Tic();
//allow the external caller to enforce dT
if (forceDt != -1) {
dT = forceDt;
}
//store this for corrections
m_dLastDt = dT;
//this is a great reference: http://adg.stanford.edu/aa208/dynamics/eom.html
//calcualte the 3 accelerations based on the force (in body coordinates)
Eigen::Vector3d accel = force / m_dMass - m_vW.cross(m_vW);
/*
//enfore holonomic constraints by applying sideways forces
//first we have to rotate velocity into body frame
Eigen::Vector3d vBodyV = R.transpose()*m_vV;
//calculate the acceleration required to remove this component
Eigen::Vector3d vNhAccel;
vNhAccel << 0, vBodyV(1) / dT, 0;
//rotate the NH constraints into body coords
vNhAccel = R*vNhAccel;
//add them to the total acceleration
accel += vNhAccel;
*/
//double integrate to get new velocity/position
m_vV += (accel * dT);
m_vLastPosition = m_vPosition;
m_vPosition += (m_vV * dT);
Eigen::Vector3d waccel = m_vII * torque + m_vII * (m_vW.cross(m_vII * m_vW));
//double integrate to get new angular velocity/rotation
m_vW += (waccel * dT);
m_vLastRotation = m_vRotation;
m_vRotation += (m_vW * dT);
}
/*
float acceleration(const State &state, float t) {
const float k = 10;
const float b = 1;
return -k * state.x - b * state.v;
}
/////////////////////////////////////////////////////////////////////////////////////////
Derivative evaluate(const State &initial, float dt, const Derivative &d) {
State state;
state.x = initial.x + d.dx*dt;
state.v = initial.v + d.dv*dt;
Derivative output;
output.dx = state.v;
output.dv = acceleration(state, t + dt);
return output;
}
void integrate(State &state, float dt) {
Derivative a = evaluate(state, 0.0f, Derivative());
Derivative b = evaluate(state, dt * 0.5f, a);
Derivative c = evaluate(state, dt * 0.5f, b);
Derivative d = evaluate(state, dt, c);
const float dxdt = 1.0f / 6.0f * (a.dx + 2.0f * (b.dx + c.dx) + d.dx);
const float dvdt = 1.0f / 6.0f * (a.dv + 2.0f * (b.dv + c.dv) + d.dv)
state.x = state.x + dxdt * dt;
state.v = state.v + dvdt * dt;
}
*/
Eigen::Vector3d GetPosition() {
return m_vPosition;
}
Eigen::Vector3d GetRotation() {
return m_vRotation;
}
void SetPosition(Eigen::Vector3d pos) {
m_vPosition = pos;
}
void SetRotation(Eigen::Vector3d rot) {
m_vRotation = rot;
}
void CorrectPosition(Eigen::Vector3d pos) {
//augment the velocity vector with this correction
m_vV = (pos - m_vLastPosition) / m_dLastDt;
m_vPosition = pos;
}
void CorrectRotation(Eigen::Vector3d rot) {
m_vW = (rot - m_vLastRotation) / m_dLastDt;
m_vRotation = rot;
}
private:
Eigen::Vector3d m_vPosition;
Eigen::Vector3d m_vLastPosition;
Eigen::Vector3d m_vRotation;
Eigen::Vector3d m_vLastRotation;
Eigen::Vector3d m_vV;
Eigen::Vector3d m_vW;
Eigen::Matrix3d m_vI;
Eigen::Matrix3d m_vII;
double m_dMass;
double m_dTime;
double m_dLastDt;
Eigen::Vector3d m_vG;
};
#endif // RIGIDBODY_H