b2PrismaticJoint.cpp

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/*
* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
*
* This software is provided 'as-is', without any express or implied
* warranty.  In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/

#include <Box2D/Dynamics/Joints/b2PrismaticJoint.h>
#include <Box2D/Dynamics/b2Body.h>
#include <Box2D/Dynamics/b2TimeStep.h>

// Linear constraint (point-to-line)
// d = p2 - p1 = x2 + r2 - x1 - r1
// C = dot(perp, d)
// Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
//      = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
// J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
//
// Angular constraint
// C = a2 - a1 + a_initial
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
//
// K = J * invM * JT
//
// J = [-a -s1 a s2]
//     [0  -1  0  1]
// a = perp
// s1 = cross(d + r1, a) = cross(p2 - x1, a)
// s2 = cross(r2, a) = cross(p2 - x2, a)


// Motor/Limit linear constraint
// C = dot(ax1, d)
// Cdot = = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
// J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]

// Block Solver
// We develop a block solver that includes the joint limit. This makes the limit stiff (inelastic) even
// when the mass has poor distribution (leading to large torques about the joint anchor points).
//
// The Jacobian has 3 rows:
// J = [-uT -s1 uT s2] // linear
//     [0   -1   0  1] // angular
//     [-vT -a1 vT a2] // limit
//
// u = perp
// v = axis
// s1 = cross(d + r1, u), s2 = cross(r2, u)
// a1 = cross(d + r1, v), a2 = cross(r2, v)

// M * (v2 - v1) = JT * df
// J * v2 = bias
//
// v2 = v1 + invM * JT * df
// J * (v1 + invM * JT * df) = bias
// K * df = bias - J * v1 = -Cdot
// K = J * invM * JT
// Cdot = J * v1 - bias
//
// Now solve for f2.
// df = f2 - f1
// K * (f2 - f1) = -Cdot
// f2 = invK * (-Cdot) + f1
//
// Clamp accumulated limit impulse.
// lower: f2(3) = max(f2(3), 0)
// upper: f2(3) = min(f2(3), 0)
//
// Solve for correct f2(1:2)
// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:3) * f1
//                       = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:2) * f1(1:2) + K(1:2,3) * f1(3)
// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3)) + K(1:2,1:2) * f1(1:2)
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
//
// Now compute impulse to be applied:
// df = f2 - f1

void b2PrismaticJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor, const b2Vec2& axis)
{
        bodyA = bA;
        bodyB = bB;
        localAnchorA = bodyA->GetLocalPoint(anchor);
        localAnchorB = bodyB->GetLocalPoint(anchor);
        localAxisA = bodyA->GetLocalVector(axis);
        referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
}

b2PrismaticJoint::b2PrismaticJoint(const b2PrismaticJointDef* def)
: b2Joint(def)
{
        m_localAnchorA = def->localAnchorA;
        m_localAnchorB = def->localAnchorB;
        m_localXAxisA = def->localAxisA;
        m_localXAxisA.Normalize();
        m_localYAxisA = b2Cross(1.0f, m_localXAxisA);
        m_referenceAngle = def->referenceAngle;

        m_impulse.SetZero();
        m_motorMass = 0.0f;
        m_motorImpulse = 0.0f;

        m_lowerTranslation = def->lowerTranslation;
        m_upperTranslation = def->upperTranslation;
        m_maxMotorForce = def->maxMotorForce;
        m_motorSpeed = def->motorSpeed;
        m_enableLimit = def->enableLimit;
        m_enableMotor = def->enableMotor;
        m_limitState = e_inactiveLimit;

        m_axis.SetZero();
        m_perp.SetZero();
}

void b2PrismaticJoint::InitVelocityConstraints(const b2SolverData& data)
{
        m_indexA = m_bodyA->m_islandIndex;
        m_indexB = m_bodyB->m_islandIndex;
        m_localCenterA = m_bodyA->m_sweep.localCenter;
        m_localCenterB = m_bodyB->m_sweep.localCenter;
        m_invMassA = m_bodyA->m_invMass;
        m_invMassB = m_bodyB->m_invMass;
        m_invIA = m_bodyA->m_invI;
        m_invIB = m_bodyB->m_invI;

        b2Vec2 cA = data.positions[m_indexA].c;
        float32 aA = data.positions[m_indexA].a;
        b2Vec2 vA = data.velocities[m_indexA].v;
        float32 wA = data.velocities[m_indexA].w;

        b2Vec2 cB = data.positions[m_indexB].c;
        float32 aB = data.positions[m_indexB].a;
        b2Vec2 vB = data.velocities[m_indexB].v;
        float32 wB = data.velocities[m_indexB].w;

        b2Rot qA(aA), qB(aB);

        // Compute the effective masses.
        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        b2Vec2 d = (cB - cA) + rB - rA;

        float32 mA = m_invMassA, mB = m_invMassB;
        float32 iA = m_invIA, iB = m_invIB;

        // Compute motor Jacobian and effective mass.
        {
                m_axis = b2Mul(qA, m_localXAxisA);
                m_a1 = b2Cross(d + rA, m_axis);
                m_a2 = b2Cross(rB, m_axis);

                m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
                if (m_motorMass > 0.0f)
                {
                        m_motorMass = 1.0f / m_motorMass;
                }
        }

        // Prismatic constraint.
        {
                m_perp = b2Mul(qA, m_localYAxisA);

                m_s1 = b2Cross(d + rA, m_perp);
                m_s2 = b2Cross(rB, m_perp);

        float32 s1test;
        s1test = b2Cross(rA, m_perp);

                float32 k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
                float32 k12 = iA * m_s1 + iB * m_s2;
                float32 k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
                float32 k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        // For bodies with fixed rotation.
                        k22 = 1.0f;
                }
                float32 k23 = iA * m_a1 + iB * m_a2;
                float32 k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;

                m_K.ex.Set(k11, k12, k13);
                m_K.ey.Set(k12, k22, k23);
                m_K.ez.Set(k13, k23, k33);
        }

        // Compute motor and limit terms.
        if (m_enableLimit)
        {
                float32 jointTranslation = b2Dot(m_axis, d);
                if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
                {
                        m_limitState = e_equalLimits;
                }
                else if (jointTranslation <= m_lowerTranslation)
                {
                        if (m_limitState != e_atLowerLimit)
                        {
                                m_limitState = e_atLowerLimit;
                                m_impulse.z = 0.0f;
                        }
                }
                else if (jointTranslation >= m_upperTranslation)
                {
                        if (m_limitState != e_atUpperLimit)
                        {
                                m_limitState = e_atUpperLimit;
                                m_impulse.z = 0.0f;
                        }
                }
                else
                {
                        m_limitState = e_inactiveLimit;
                        m_impulse.z = 0.0f;
                }
        }
        else
        {
                m_limitState = e_inactiveLimit;
                m_impulse.z = 0.0f;
        }

        if (m_enableMotor == false)
        {
                m_motorImpulse = 0.0f;
        }

        if (data.step.warmStarting)
        {
                // Account for variable time step.
                m_impulse *= data.step.dtRatio;
                m_motorImpulse *= data.step.dtRatio;

                b2Vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis;
                float32 LA = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
                float32 LB = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;

                vA -= mA * P;
                wA -= iA * LA;

                vB += mB * P;
                wB += iB * LB;
        }
        else
        {
                m_impulse.SetZero();
                m_motorImpulse = 0.0f;
        }

        data.velocities[m_indexA].v = vA;
        data.velocities[m_indexA].w = wA;
        data.velocities[m_indexB].v = vB;
        data.velocities[m_indexB].w = wB;
}

void b2PrismaticJoint::SolveVelocityConstraints(const b2SolverData& data)
{
        b2Vec2 vA = data.velocities[m_indexA].v;
        float32 wA = data.velocities[m_indexA].w;
        b2Vec2 vB = data.velocities[m_indexB].v;
        float32 wB = data.velocities[m_indexB].w;

        float32 mA = m_invMassA, mB = m_invMassB;
        float32 iA = m_invIA, iB = m_invIB;

        // Solve linear motor constraint.
        if (m_enableMotor && m_limitState != e_equalLimits)
        {
                float32 Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
                float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
                float32 oldImpulse = m_motorImpulse;
                float32 maxImpulse = data.step.dt * m_maxMotorForce;
                m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
                impulse = m_motorImpulse - oldImpulse;

                b2Vec2 P = impulse * m_axis;
                float32 LA = impulse * m_a1;
                float32 LB = impulse * m_a2;

                vA -= mA * P;
                wA -= iA * LA;

                vB += mB * P;
                wB += iB * LB;
        }

        b2Vec2 Cdot1;
        Cdot1.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
        Cdot1.y = wB - wA;

        if (m_enableLimit && m_limitState != e_inactiveLimit)
        {
                // Solve prismatic and limit constraint in block form.
                float32 Cdot2;
                Cdot2 = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
                b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);

                b2Vec3 f1 = m_impulse;
                b2Vec3 df =  m_K.Solve33(-Cdot);
                m_impulse += df;

                if (m_limitState == e_atLowerLimit)
                {
                        m_impulse.z = b2Max(m_impulse.z, 0.0f);
                }
                else if (m_limitState == e_atUpperLimit)
                {
                        m_impulse.z = b2Min(m_impulse.z, 0.0f);
                }

                // f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
                b2Vec2 b = -Cdot1 - (m_impulse.z - f1.z) * b2Vec2(m_K.ez.x, m_K.ez.y);
                b2Vec2 f2r = m_K.Solve22(b) + b2Vec2(f1.x, f1.y);
                m_impulse.x = f2r.x;
                m_impulse.y = f2r.y;

                df = m_impulse - f1;

                b2Vec2 P = df.x * m_perp + df.z * m_axis;
                float32 LA = df.x * m_s1 + df.y + df.z * m_a1;
                float32 LB = df.x * m_s2 + df.y + df.z * m_a2;

                vA -= mA * P;
                wA -= iA * LA;

                vB += mB * P;
                wB += iB * LB;
        }
        else
        {
                // Limit is inactive, just solve the prismatic constraint in block form.
                b2Vec2 df = m_K.Solve22(-Cdot1);
                m_impulse.x += df.x;
                m_impulse.y += df.y;

                b2Vec2 P = df.x * m_perp;
                float32 LA = df.x * m_s1 + df.y;
                float32 LB = df.x * m_s2 + df.y;

                vA -= mA * P;
                wA -= iA * LA;

                vB += mB * P;
                wB += iB * LB;
        }

        data.velocities[m_indexA].v = vA;
        data.velocities[m_indexA].w = wA;
        data.velocities[m_indexB].v = vB;
        data.velocities[m_indexB].w = wB;
}

bool b2PrismaticJoint::SolvePositionConstraints(const b2SolverData& data)
{
        b2Vec2 cA = data.positions[m_indexA].c;
        float32 aA = data.positions[m_indexA].a;
        b2Vec2 cB = data.positions[m_indexB].c;
        float32 aB = data.positions[m_indexB].a;

        b2Rot qA(aA), qB(aB);

        float32 mA = m_invMassA, mB = m_invMassB;
        float32 iA = m_invIA, iB = m_invIB;

        // Compute fresh Jacobians
        b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
        b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
        b2Vec2 d = cB + rB - cA - rA;

        b2Vec2 axis = b2Mul(qA, m_localXAxisA);
        float32 a1 = b2Cross(d + rA, axis);
        float32 a2 = b2Cross(rB, axis);
        b2Vec2 perp = b2Mul(qA, m_localYAxisA);

        float32 s1 = b2Cross(d + rA, perp);
        float32 s2 = b2Cross(rB, perp);

        b2Vec3 impulse;
        b2Vec2 C1;
        C1.x = b2Dot(perp, d);
        C1.y = aB - aA - m_referenceAngle;

        float32 linearError = b2Abs(C1.x);
        float32 angularError = b2Abs(C1.y);

        bool active = false;
        float32 C2 = 0.0f;
        if (m_enableLimit)
        {
                float32 translation = b2Dot(axis, d);
                if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
                {
                        // Prevent large angular corrections
                        C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
                        linearError = b2Max(linearError, b2Abs(translation));
                        active = true;
                }
                else if (translation <= m_lowerTranslation)
                {
                        // Prevent large linear corrections and allow some slop.
                        C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
                        linearError = b2Max(linearError, m_lowerTranslation - translation);
                        active = true;
                }
                else if (translation >= m_upperTranslation)
                {
                        // Prevent large linear corrections and allow some slop.
                        C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
                        linearError = b2Max(linearError, translation - m_upperTranslation);
                        active = true;
                }
        }

        if (active)
        {
                float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
                float32 k12 = iA * s1 + iB * s2;
                float32 k13 = iA * s1 * a1 + iB * s2 * a2;
                float32 k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        // For fixed rotation
                        k22 = 1.0f;
                }
                float32 k23 = iA * a1 + iB * a2;
                float32 k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;

                b2Mat33 K;
                K.ex.Set(k11, k12, k13);
                K.ey.Set(k12, k22, k23);
                K.ez.Set(k13, k23, k33);

                b2Vec3 C;
                C.x = C1.x;
                C.y = C1.y;
                C.z = C2;

                impulse = K.Solve33(-C);
        }
        else
        {
                float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
                float32 k12 = iA * s1 + iB * s2;
                float32 k22 = iA + iB;
                if (k22 == 0.0f)
                {
                        k22 = 1.0f;
                }

                b2Mat22 K;
                K.ex.Set(k11, k12);
                K.ey.Set(k12, k22);

                b2Vec2 impulse1 = K.Solve(-C1);
                impulse.x = impulse1.x;
                impulse.y = impulse1.y;
                impulse.z = 0.0f;
        }

        b2Vec2 P = impulse.x * perp + impulse.z * axis;
        float32 LA = impulse.x * s1 + impulse.y + impulse.z * a1;
        float32 LB = impulse.x * s2 + impulse.y + impulse.z * a2;

        cA -= mA * P;
        aA -= iA * LA;
        cB += mB * P;
        aB += iB * LB;

        data.positions[m_indexA].c = cA;
        data.positions[m_indexA].a = aA;
        data.positions[m_indexB].c = cB;
        data.positions[m_indexB].a = aB;

        return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}

b2Vec2 b2PrismaticJoint::GetAnchorA() const
{
        return m_bodyA->GetWorldPoint(m_localAnchorA);
}

b2Vec2 b2PrismaticJoint::GetAnchorB() const
{
        return m_bodyB->GetWorldPoint(m_localAnchorB);
}

b2Vec2 b2PrismaticJoint::GetReactionForce(float32 inv_dt) const
{
        return inv_dt * (m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis);
}

float32 b2PrismaticJoint::GetReactionTorque(float32 inv_dt) const
{
        return inv_dt * m_impulse.y;
}

float32 b2PrismaticJoint::GetJointTranslation() const
{
        b2Vec2 pA = m_bodyA->GetWorldPoint(m_localAnchorA);
        b2Vec2 pB = m_bodyB->GetWorldPoint(m_localAnchorB);
        b2Vec2 d = pB - pA;
        b2Vec2 axis = m_bodyA->GetWorldVector(m_localXAxisA);

        float32 translation = b2Dot(d, axis);
        return translation;
}

float32 b2PrismaticJoint::GetJointSpeed() const
{
        b2Body* bA = m_bodyA;
        b2Body* bB = m_bodyB;

        b2Vec2 rA = b2Mul(bA->m_xf.q, m_localAnchorA - bA->m_sweep.localCenter);
        b2Vec2 rB = b2Mul(bB->m_xf.q, m_localAnchorB - bB->m_sweep.localCenter);
        b2Vec2 p1 = bA->m_sweep.c + rA;
        b2Vec2 p2 = bB->m_sweep.c + rB;
        b2Vec2 d = p2 - p1;
        b2Vec2 axis = b2Mul(bA->m_xf.q, m_localXAxisA);

        b2Vec2 vA = bA->m_linearVelocity;
        b2Vec2 vB = bB->m_linearVelocity;
        float32 wA = bA->m_angularVelocity;
        float32 wB = bB->m_angularVelocity;

        float32 speed = b2Dot(d, b2Cross(wA, axis)) + b2Dot(axis, vB + b2Cross(wB, rB) - vA - b2Cross(wA, rA));
        return speed;
}

bool b2PrismaticJoint::IsLimitEnabled() const
{
        return m_enableLimit;
}

void b2PrismaticJoint::EnableLimit(bool flag)
{
        if (flag != m_enableLimit)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_enableLimit = flag;
                m_impulse.z = 0.0f;
        }
}

float32 b2PrismaticJoint::GetLowerLimit() const
{
        return m_lowerTranslation;
}

float32 b2PrismaticJoint::GetUpperLimit() const
{
        return m_upperTranslation;
}

void b2PrismaticJoint::SetLimits(float32 lower, float32 upper)
{
        b2Assert(lower <= upper);
        if (lower != m_lowerTranslation || upper != m_upperTranslation)
        {
                m_bodyA->SetAwake(true);
                m_bodyB->SetAwake(true);
                m_lowerTranslation = lower;
                m_upperTranslation = upper;
                m_impulse.z = 0.0f;
        }
}

bool b2PrismaticJoint::IsMotorEnabled() const
{
        return m_enableMotor;
}

void b2PrismaticJoint::EnableMotor(bool flag)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_enableMotor = flag;
}

void b2PrismaticJoint::SetMotorSpeed(float32 speed)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_motorSpeed = speed;
}

void b2PrismaticJoint::SetMaxMotorForce(float32 force)
{
        m_bodyA->SetAwake(true);
        m_bodyB->SetAwake(true);
        m_maxMotorForce = force;
}

float32 b2PrismaticJoint::GetMotorForce(float32 inv_dt) const
{
        return inv_dt * m_motorImpulse;
}

void b2PrismaticJoint::Dump()
{
        int32 indexA = m_bodyA->m_islandIndex;
        int32 indexB = m_bodyB->m_islandIndex;

        b2Log("  b2PrismaticJointDef jd;\n");
        b2Log("  jd.bodyA = bodies[%d];\n", indexA);
        b2Log("  jd.bodyB = bodies[%d];\n", indexB);
        b2Log("  jd.collideConnected = bool(%d);\n", m_collideConnected);
        b2Log("  jd.localAnchorA.Set(%.15lef, %.15lef);\n", m_localAnchorA.x, m_localAnchorA.y);
        b2Log("  jd.localAnchorB.Set(%.15lef, %.15lef);\n", m_localAnchorB.x, m_localAnchorB.y);
        b2Log("  jd.localAxisA.Set(%.15lef, %.15lef);\n", m_localXAxisA.x, m_localXAxisA.y);
        b2Log("  jd.referenceAngle = %.15lef;\n", m_referenceAngle);
        b2Log("  jd.enableLimit = bool(%d);\n", m_enableLimit);
        b2Log("  jd.lowerTranslation = %.15lef;\n", m_lowerTranslation);
        b2Log("  jd.upperTranslation = %.15lef;\n", m_upperTranslation);
        b2Log("  jd.enableMotor = bool(%d);\n", m_enableMotor);
        b2Log("  jd.motorSpeed = %.15lef;\n", m_motorSpeed);
        b2Log("  jd.maxMotorForce = %.15lef;\n", m_maxMotorForce);
        b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
}