ForwardDynamicsCBM.cpp

/*
 * Copyright (c) 2008, AIST, the University of Tokyo and General Robotix Inc.
 * All rights reserved. This program is made available under the terms of the
 * Eclipse Public License v1.0 which accompanies this distribution, and is
 * available at http://www.eclipse.org/legal/epl-v10.html
 * Contributors:
 * National Institute of Advanced Industrial Science and Technology (AIST)
 */
/**
   \file
   \author Shin'ichiro Nakaoka
*/

#include "Body.h"
#include "Link.h"
#include "LinkTraverse.h"
#include "Sensor.h"
#include "ForwardDynamicsCBM.h"

using namespace hrp;
using namespace std;


static const bool CALC_ALL_JOINT_TORQUES = false;
static const bool ROOT_ATT_NORMALIZATION_ENABLED = false;

static const bool debugMode = false;

#include <boost/format.hpp>

template<class TMatrix>
static void putMatrix(TMatrix& M, char* name)
{
	if(M.cols() == 1){
		std::cout << "Vector " << name << M << std::endl;
	} else {
		std::cout << "Matrix " << name << ": \n";
		for(size_t i=0; i < M.size1(); i++){
			for(size_t j=0; j < M.cols(); j++){
				std::cout << boost::format(" %6.3f ") % M(i, j);
			}
			std::cout << std::endl;
		}
	}
}

template<class TVector>
static void putVector(TVector& M, char* name)
{
	std::cout << "Vector " << name << M << std::endl;
}


ForwardDynamicsMM::ForwardDynamicsMM(BodyPtr body) :
    ForwardDynamics(body)
{

}


ForwardDynamicsMM::~ForwardDynamicsMM()
{

}


void ForwardDynamicsMM::initialize()
{
    Link* root = body->rootLink();
	unknown_rootDof = (root->jointType == Link::FREE_JOINT && !root->isHighGainMode ) ? 6 : 0;
    given_rootDof = (root->jointType == Link::FREE_JOINT && root->isHighGainMode ) ? 6 : 0;

	torqueModeJoints.clear();
	highGainModeJoints.clear();

	int numLinks = body->numLinks();

	for(int i=1; i < numLinks; ++i){
		Link* link = body->link(i);
		int jointType = link->jointType;
		if(jointType == Link::ROTATIONAL_JOINT || jointType == Link::SLIDE_JOINT){
			if(link->isHighGainMode){
				highGainModeJoints.push_back(link);
			} else {
				torqueModeJoints.push_back(link);
			}
		}
	}

	int n = unknown_rootDof + torqueModeJoints.size();
	int m = highGainModeJoints.size();
    
	isNoUnknownAccelMode = (n == 0);

	M11.resize(n, n);
	M12.resize(n, given_rootDof+m);
	b1. resize(n, 1);
	c1. resize(n);
    d1. resize(n, 1);

	qGiven.  resize(m);
	dqGiven. resize(m);
	ddqGiven.resize(given_rootDof+m, 1);

	qGivenPrev. resize(m);
	dqGivenPrev.resize(m);

	ddqorg.resize(numLinks);
	uorg.  resize(numLinks);

	calcPositionAndVelocityFK();

	if(!isNoUnknownAccelMode){
		calcMassMatrix();
	}

	ddqGivenCopied = false;

	initializeSensors();

	if(integrationMode == RUNGEKUTTA_METHOD){

		q0. resize(numLinks);
		dq0.resize(numLinks);
		dq. resize(numLinks);
		ddq.resize(numLinks);

		preserveHighGainModeJointState();
	}
}


void ForwardDynamicsMM::solveUnknownAccels()
{
    if(!isNoUnknownAccelMode){
    	initializeAccelSolver();
	    solveUnknownAccels(fextTotal, tauextTotal);
    }
}


inline void ForwardDynamicsMM::calcAccelFKandForceSensorValues()
{
	Vector3 f, tau;
	calcAccelFKandForceSensorValues(body->rootLink(), f, tau);
}


void ForwardDynamicsMM::calcNextState()
{
	if(isNoUnknownAccelMode && !body->numSensors(Sensor::FORCE)){

		calcPositionAndVelocityFK();

	} else {

		switch(integrationMode){

		case EULER_METHOD:
			calcMotionWithEulerMethod();
			break;
			
		case RUNGEKUTTA_METHOD:
			calcMotionWithRungeKuttaMethod();
			break;
		}
		
		if(ROOT_ATT_NORMALIZATION_ENABLED && unknown_rootDof){
                        Matrix33& R = body->rootLink()->R;
                        Matrix33::ColXpr x = R.col(0);
                        Matrix33::ColXpr y = R.col(1);
                        Matrix33::ColXpr z = R.col(2);
                        x.normalize();
                        z = x.cross(y).normalized();
                        y = z.cross(x);
		}
	}
		
	if(sensorsEnabled){
		updateSensorsFinal();
	}
	
	body->setVirtualJointForces();

	ddqGivenCopied = false;
}


void ForwardDynamicsMM::calcMotionWithEulerMethod()
{
	sumExternalForces();
	solveUnknownAccels();
	calcAccelFKandForceSensorValues();

    Link* root = body->rootLink();

    if(unknown_rootDof){
        Vector3  p;
        Matrix33 R;
        SE3exp(p, R, root->p, root->R, root->w, root->vo, timeStep);
        root->p = p;
        root->R = R;

        root->vo += root->dvo * timeStep;
		root->w  += root->dw  * timeStep;
    }

	int n = torqueModeJoints.size();
	for(int i=0; i < n; ++i){
		Link* link = torqueModeJoints[i];
		link->q  += link->dq  * timeStep;
        link->dq += link->ddq * timeStep;
	}

	calcPositionAndVelocityFK();
	calcMassMatrix();
}


void ForwardDynamicsMM::calcMotionWithRungeKuttaMethod()
{
	int numHighGainJoints = highGainModeJoints.size();
    Link* root = body->rootLink();

    if(given_rootDof){
        pGiven = root->p;
        RGiven = root->R;
        voGiven = root->vo;
        wGiven = root->w;
        root->p = pGivenPrev;
        root->R = RGivenPrev;
        root->vo = voGivenPrev;
        root->w = wGivenPrev;
    }

	for(int i=0; i < numHighGainJoints; ++i){
		Link* link = highGainModeJoints[i];
		qGiven [i] = link->q;
		dqGiven[i] = link->dq;
		link->q  = qGivenPrev[i];
		link->dq = dqGivenPrev[i];
	}
  
    if(unknown_rootDof || given_rootDof){
		p0  = root->p;
		R0  = root->R;
		vo0 = root->vo;
		w0  = root->w;
    }

    vo.setZero();
    w.setZero();
    dvo.setZero();
    dw.setZero();

	int numLinks = body->numLinks();

	for(int i=1; i < numLinks; ++i){
		Link* link = body->link(i);
        q0 [i] = link->q;
		dq0[i] = link->dq;
		dq [i] = 0.0;
		ddq[i] = 0.0;
	}

	sumExternalForces();

	solveUnknownAccels();
	calcAccelFKandForceSensorValues();

    integrateRungeKuttaOneStep(1.0 / 6.0, timeStep / 2.0);

	calcPositionAndVelocityFK();
	calcMassMatrix();
	solveUnknownAccels();

    integrateRungeKuttaOneStep(2.0 / 6.0, timeStep / 2.0);

	calcPositionAndVelocityFK();
	calcMassMatrix();
	solveUnknownAccels();

    integrateRungeKuttaOneStep(2.0 / 6.0, timeStep);

	calcPositionAndVelocityFK();
	calcMassMatrix();
	solveUnknownAccels();

    if(unknown_rootDof){
        SE3exp(root->p, root->R, p0, R0, w0, vo0, timeStep);
        root->vo = vo0 + (dvo + root->dvo / 6.0) * timeStep;
		root->w  = w0  + (dw  + root->dw  / 6.0) * timeStep;
    }
    if(given_rootDof){
        root->p = pGiven;
        root->R = RGiven;
        root->vo = voGiven;
        root->w = wGiven;
    }

    for(size_t i=0; i < torqueModeJoints.size(); ++i){
		Link* link = torqueModeJoints[i];
		int index = link->index;
		link->q  = q0 [index] + (dq [index] + link->dq  / 6.0) * timeStep;
		link->dq = dq0[index] + (ddq[index] + link->ddq / 6.0) * timeStep;
    }
	for(size_t i=0; i < highGainModeJoints.size(); ++i){
		Link* link = highGainModeJoints[i];
		link->q  = qGiven [i];
		link->dq = dqGiven[i];
	}

	calcPositionAndVelocityFK();
	calcMassMatrix();

	preserveHighGainModeJointState();
}


void ForwardDynamicsMM::integrateRungeKuttaOneStep(double r, double dt)
{
    Link* root = body->rootLink();

    if(unknown_rootDof || given_rootDof){
        SE3exp(root->p, root->R, p0, R0, root->w, root->vo, dt);
        root->vo = vo0 + root->dvo * dt;
		root->w  = w0  + root->dw  * dt;

		vo  += r * root->vo;
		w   += r * root->w;
		dvo += r * root->dvo;
		dw  += r * root->dw;
    }

	int n = body->numLinks();
	for(int i=1; i < n; ++i){
		Link* link = body->link(i);
		link->q  = q0 [i] + dt * link->dq;
		link->dq = dq0[i] + dt * link->ddq;
		dq [i] += r * link->dq;
		ddq[i] += r * link->ddq;
	}
}


void ForwardDynamicsMM::preserveHighGainModeJointState()
{
    if(given_rootDof){
        Link* root = body->rootLink();
        pGivenPrev = root->p;
        RGivenPrev = root->R;
        voGivenPrev = root->vo;
        wGivenPrev = root->w;
    }
    for(size_t i=0; i < highGainModeJoints.size(); ++i){
		Link* link = highGainModeJoints[i];
		qGivenPrev [i] = link->q;
		dqGivenPrev[i] = link->dq;
	}
}


void ForwardDynamicsMM::calcPositionAndVelocityFK()
{
    const LinkTraverse& traverse = body->linkTraverse();
    int n = traverse.numLinks();

	Link* root = traverse[0];
	root_w_x_v = root->w.cross(root->vo + root->w.cross(root->p));
    
    if(given_rootDof){
        root->vo = root->v - root->w.cross(root->p);
    }

    for(int i=0; i < n; ++i){
        Link* link = traverse[i];
        Link* parent = link->parent;

		if(parent){

			switch(link->jointType){

			case Link::SLIDE_JOINT:
				link->p  = parent->R * (link->b + link->q * link->d) + parent->p;
				link->R  = parent->R;
				link->sw.setZero();
				link->sv.noalias() = parent->R * link->d;
				link->w  = parent->w;
				break;

			case Link::ROTATIONAL_JOINT:
                                link->R.noalias()  = parent->R * rodrigues(link->a, link->q);
				link->p  = parent->R * link->b + parent->p;
				link->sw.noalias() = parent->R * link->a;
				link->sv = link->p.cross(link->sw);
				link->w  = link->dq * link->sw + parent->w;
				break;

            case Link::FIXED_JOINT:
            default:
				link->p = parent->R * link->b + parent->p;
				link->R = parent->R;
				link->w = parent->w;
				link->vo = parent->vo;
				link->sw.setZero();
				link->sv.setZero();
				link->cv.setZero();
				link->cw.setZero();
                goto COMMON_CALCS_FOR_ALL_JOINT_TYPES;
			}

			link->vo = link->dq * link->sv + parent->vo;

			Vector3 dsv(parent->w.cross(link->sv) + parent->vo.cross(link->sw));
			Vector3 dsw(parent->w.cross(link->sw));
			link->cv = link->dq * dsv;
			link->cw = link->dq * dsw;
		}

        COMMON_CALCS_FOR_ALL_JOINT_TYPES:

		/// \todo remove this  equation
		link->v = link->vo + link->w.cross(link->p);

		link->wc = link->R * link->c + link->p;
		Matrix33 Iw(link->R * link->I * link->R.transpose());
        Matrix33 c_hat(hat(link->wc));
                link->Iww = link->m * (c_hat * c_hat.transpose()) + Iw;
		link->Iwv = link->m * c_hat;

		Vector3 P(link->m * (link->vo + link->w.cross(link->wc)));
		Vector3 L(link->Iww * link->w + link->m * link->wc.cross(link->vo));

		link->pf   = link->w.cross(P);
		link->ptau = link->vo.cross(P) + link->w.cross(L);
        
    }
}


/**
   calculate the mass matrix using the unit vector method
   \todo replace the unit vector method here with
   a more efficient method that only requires O(n) computation time
*/
void ForwardDynamicsMM::calcMassMatrix()
{
	Link* root = body->rootLink();
	int numLinks = body->numLinks();

	// preserve and clear the joint accelerations
	for(int i=1; i < numLinks; ++i){
		Link* link = body->link(i);
		ddqorg[i] = link->ddq;
		uorg  [i] = link->u;
		link->ddq = 0.0;
	}

	// preserve and clear the root link acceleration
	dvoorg = root->dvo;
	dworg  = root->dw;
	root->dvo = g - root_w_x_v;   // dv = g, dw = 0
	root->dw.setZero();
	
	setColumnOfMassMatrix(b1, 0);

	if(unknown_rootDof){
		for(int i=0; i < 3; ++i){
			root->dvo[i] += 1.0;
			setColumnOfMassMatrix(M11, i);
			root->dvo[i] -= 1.0;
		}
		for(int i=0; i < 3; ++i){
			root->dw[i] = 1.0;
			Vector3 dw_x_p = root->dw.cross(root->p);
			root->dvo -= dw_x_p;
			setColumnOfMassMatrix(M11, i + 3);
			root->dvo += dw_x_p;
			root->dw[i] = 0.0;
		}
	}
    if(given_rootDof){
        for(int i=0; i < 3; ++i){
			root->dvo[i] += 1.0;
			setColumnOfMassMatrix(M12, i);
			root->dvo[i] -= 1.0;
		}
		for(int i=0; i < 3; ++i){
			root->dw[i] = 1.0;
			Vector3 dw_x_p = root->dw.cross(root->p);
			root->dvo -= dw_x_p;
			setColumnOfMassMatrix(M12, i + 3);
			root->dvo += dw_x_p;
			root->dw[i] = 0.0;
		}
    }

	for(size_t i=0; i < torqueModeJoints.size(); ++i){
		Link* link = torqueModeJoints[i];
		link->ddq = 1.0;
		int j = i + unknown_rootDof;
		setColumnOfMassMatrix(M11, j);
		M11(j, j) += link->Jm2; // motor inertia
		link->ddq = 0.0;
    }
    for(size_t i=0; i < highGainModeJoints.size(); ++i){
		Link* link = highGainModeJoints[i];
		link->ddq = 1.0;
        int j = i + given_rootDof;
		setColumnOfMassMatrix(M12, j);
		link->ddq = 0.0;
    }

	// subtract the constant term
	for(int i=0; i < M11.cols(); ++i){
            M11.col(i) -= b1;
	}
	for(int i=0; i < M12.cols(); ++i){
            M12.col(i) -= b1;
	}

	for(int i=1; i < numLinks; ++i){
		Link* link = body->link(i);
		link->ddq = ddqorg[i];
		link->u   = uorg  [i];
	}
	root->dvo = dvoorg;
	root->dw  = dworg;

	accelSolverInitialized = false;
}


void ForwardDynamicsMM::setColumnOfMassMatrix(dmatrix& M, int column)
{
    Vector3 f;
	Vector3 tau;
    Link* root = body->rootLink();
    calcInverseDynamics(root, f, tau);

	if(unknown_rootDof){
                tau -= root->p.cross(f);
                M.block<6,1>(0, column) << f, tau;
	}

	for(size_t i=0; i < torqueModeJoints.size(); ++i){
		M(i + unknown_rootDof, column) = torqueModeJoints[i]->u;
    }
}


void ForwardDynamicsMM::calcInverseDynamics(Link* link, Vector3& out_f, Vector3& out_tau)
{
    Link* parent = link->parent;
    if(parent){
		link->dvo = parent->dvo + link->cv + link->sv * link->ddq;
		link->dw  = parent->dw  + link->cw + link->sw * link->ddq;
    }

    out_f = link->pf;
    out_tau = link->ptau;

    if(link->child){
		Vector3 f_c;
		Vector3 tau_c;
		calcInverseDynamics(link->child, f_c, tau_c);
		out_f += f_c;
		out_tau += tau_c;
    }

    out_f   += link->m   * link->dvo + link->Iwv.transpose() * link->dw;
    out_tau += link->Iwv * link->dvo + link->Iww        * link->dw;

    link->u = link->sv.dot(out_f) + link->sw.dot(out_tau);

    if(link->sibling){
		Vector3 f_s;
		Vector3 tau_s;
		calcInverseDynamics(link->sibling, f_s, tau_s);
		out_f += f_s;
		out_tau += tau_s;
    }
}


void ForwardDynamicsMM::sumExternalForces()
{
    fextTotal.setZero();
    tauextTotal.setZero();

    int n = body->numLinks();
    for(int i=0; i < n; ++i){
		Link* link = body->link(i);
		fextTotal   += link->fext;
		tauextTotal += link->tauext;
    }

    tauextTotal -= body->rootLink()->p.cross(fextTotal);
}

void ForwardDynamicsMM::calcd1(Link* link, Vector3& out_f, Vector3& out_tau)
{
    out_f = -link->fext;
    out_tau = -link->tauext;

    if(link->child){
		Vector3 f_c;
		Vector3 tau_c;
		calcd1(link->child, f_c, tau_c);
		out_f += f_c;
		out_tau += tau_c;
    }

    link->u = link->sv.dot(out_f) + link->sw.dot(out_tau);

    if(link->sibling){
		Vector3 f_s;
		Vector3 tau_s;
		calcd1(link->sibling, f_s, tau_s);
		out_f += f_s;
		out_tau += tau_s;
    }
}

void ForwardDynamicsMM::initializeAccelSolver()
{
	if(!accelSolverInitialized){

		if(!ddqGivenCopied){
            if(given_rootDof){
                Link* root = body->rootLink();
                root->dvo = root->dv - root->dw.cross(root->p) - root->w.cross(root->v);
                ddqGiven.head(3)      = root->dvo;
                ddqGiven.segment(3,3) = root->dw;
            }
			for(size_t i=0; i < highGainModeJoints.size(); ++i){
				ddqGiven(given_rootDof+i,0) = highGainModeJoints[i]->ddq;
			}
			ddqGivenCopied = true;
		}

		b1 += M12*ddqGiven;
        
        for(unsigned int i=1; i < body->numLinks(); ++i){
		    Link* link = body->link(i);
		    uorg  [i] = link->u;
	    }
        Vector3 f, tau;
        Link* root = body->rootLink();
        calcd1(root, f, tau);
        for(int i=0; i<unknown_rootDof; i++){
            d1(i, 0) = 0;
        }
	    for(size_t i=0; i < torqueModeJoints.size(); ++i){
		    d1(i + unknown_rootDof, 0) = torqueModeJoints[i]->u;
        }
        for(unsigned int i=1; i < body->numLinks(); ++i){
		    Link* link = body->link(i);
		    link->u = uorg  [i];
	    }

		accelSolverInitialized = true;
	}
}

//for ConstraintForceSolver 
void ForwardDynamicsMM::solveUnknownAccels(Link* link, const Vector3& fext, const Vector3& tauext, const Vector3& rootfext, const Vector3& roottauext)
{
    Vector3 fextorg = link->fext;
    Vector3 tauextorg = link->tauext;
    link->fext = fext;
    link->tauext = tauext;
    for(unsigned int i=1; i < body->numLinks(); ++i){
		Link* link = body->link(i);
		uorg  [i] = link->u;
	}
    Vector3 f, tau;
    Link* root = body->rootLink();
    calcd1(root, f, tau);
    for(int i=0; i<unknown_rootDof; i++){
        d1(i, 0) = 0;
    }
	for(size_t i=0; i < torqueModeJoints.size(); ++i){
		d1(i + unknown_rootDof, 0) = torqueModeJoints[i]->u;
    }
    for(unsigned int i=1; i < body->numLinks(); ++i){
		Link* link = body->link(i);
		link->u = uorg  [i];
	}
    link->fext = fextorg;
    link->tauext = tauextorg;

    solveUnknownAccels(rootfext,roottauext);
}

void ForwardDynamicsMM::solveUnknownAccels(const Vector3& fext, const Vector3& tauext)
{
    if(unknown_rootDof){
        c1.head(3)      = fext;
        c1.segment(3,3) = tauext;
    }

	for(size_t i=0; i < torqueModeJoints.size(); ++i){
		c1(i + unknown_rootDof) = torqueModeJoints[i]->u;
	}

        c1 -= d1;
	c1 -= b1.col(0);

        dvector a;
        if(c1.size()!=0) {
            a = M11.colPivHouseholderQr().solve(c1);
        }

	if(unknown_rootDof){
		Link* root = body->rootLink();
		root->dw = a.segment(3, 3);
		Vector3 dv = a.head(3);
		root->dvo = dv - root->dw.cross(root->p) - root_w_x_v;
	}

	for(size_t i=0; i < torqueModeJoints.size(); ++i){
		Link* link = torqueModeJoints[i];
		link->ddq = c1(i + unknown_rootDof);
	}
}


void ForwardDynamicsMM::calcAccelFKandForceSensorValues(Link* link, Vector3& out_f, Vector3& out_tau)
{
    Link* parent = link->parent;

    if(parent){
		link->dvo = parent->dvo + link->cv + link->sv * link->ddq;
		link->dw  = parent->dw  + link->cw + link->sw * link->ddq;
    }

    out_f   = link->pf;
    out_tau = link->ptau;

	for(Link* child = link->child; child; child = child->sibling){
		Vector3 f, tau;
		calcAccelFKandForceSensorValues(child, f, tau);
		out_f   += f;
		out_tau += tau;
    }

	ForceSensorInfo& info = forceSensorInfo[link->index];

	if(CALC_ALL_JOINT_TORQUES || info.hasSensorsAbove){

        Vector3 fg(-link->m * g);
        Vector3 tg(link->wc.cross(fg));

		out_f   -= fg;
		out_tau -= tg;

		out_f   -= link->fext;
		out_tau -= link->tauext;

		out_f   += link->m   * link->dvo + link->Iwv.transpose() * link->dw;
		out_tau += link->Iwv * link->dvo + link->Iww        * link->dw;

		if(CALC_ALL_JOINT_TORQUES && link->isHighGainMode){
                    link->u = link->sv.dot(out_f) + link->sw.dot(out_tau);
		}

		if(info.sensor){
			ForceSensor* sensor = info.sensor;
			Matrix33 sensorR  (link->R * sensor->localR);
			Vector3  sensorPos(link->p + link->R * sensor->localPos);
			Vector3 f(-out_f);
			sensor->f   = sensorR.transpose() * f;
			sensor->tau = sensorR.transpose() * (-out_tau - sensorPos.cross(f));
		}
	}
}


void ForwardDynamicsMM::initializeSensors()
{
	ForwardDynamics::initializeSensors();

	int n = body->numLinks();

	forceSensorInfo.resize(n);

	for(int i=0; i < n; ++i){
		forceSensorInfo[i].sensor = 0;
		forceSensorInfo[i].hasSensorsAbove = false;
	}

	if(sensorsEnabled){

		int numForceSensors = body->numSensors(Sensor::FORCE);
		for(int i=0; i < numForceSensors; ++i){
			ForceSensor* sensor = body->sensor<ForceSensor>(i);
			forceSensorInfo[sensor->link->index].sensor = sensor;
		}

		updateForceSensorInfo(body->rootLink(), false);
	}
}


void ForwardDynamicsMM::updateForceSensorInfo(Link* link, bool hasSensorsAbove)
{
	ForceSensorInfo& info = forceSensorInfo[link->index];
	hasSensorsAbove |= (info.sensor != 0);
	info.hasSensorsAbove = hasSensorsAbove;

	for(Link* child = link->child; child; child = child->sibling){
		updateForceSensorInfo(child, hasSensorsAbove);
    }
}