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Diffstat (limited to 'extern/bullet2/src/BulletDynamics/Featherstone/btMultiBody.cpp')
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diff --git a/extern/bullet2/src/BulletDynamics/Featherstone/btMultiBody.cpp b/extern/bullet2/src/BulletDynamics/Featherstone/btMultiBody.cpp new file mode 100644 index 00000000000..56a1c55d9ae --- /dev/null +++ b/extern/bullet2/src/BulletDynamics/Featherstone/btMultiBody.cpp @@ -0,0 +1,1009 @@ +/* + * PURPOSE: + * Class representing an articulated rigid body. Stores the body's + * current state, allows forces and torques to be set, handles + * timestepping and implements Featherstone's algorithm. + * + * COPYRIGHT: + * Copyright (C) Stephen Thompson, <stephen@solarflare.org.uk>, 2011-2013 + * Portions written By Erwin Coumans: replacing Eigen math library by Bullet LinearMath and a dedicated 6x6 matrix inverse (solveImatrix) + + 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 "btMultiBody.h" +#include "btMultiBodyLink.h" +#include "btMultiBodyLinkCollider.h" + +// #define INCLUDE_GYRO_TERM + +namespace { + const btScalar SLEEP_EPSILON = btScalar(0.05); // this is a squared velocity (m^2 s^-2) + const btScalar SLEEP_TIMEOUT = btScalar(2); // in seconds +} + + + + +// +// Various spatial helper functions +// + +namespace { + void SpatialTransform(const btMatrix3x3 &rotation_matrix, // rotates vectors in 'from' frame to vectors in 'to' frame + const btVector3 &displacement, // vector from origin of 'from' frame to origin of 'to' frame, in 'to' coordinates + const btVector3 &top_in, // top part of input vector + const btVector3 &bottom_in, // bottom part of input vector + btVector3 &top_out, // top part of output vector + btVector3 &bottom_out) // bottom part of output vector + { + top_out = rotation_matrix * top_in; + bottom_out = -displacement.cross(top_out) + rotation_matrix * bottom_in; + } + + void InverseSpatialTransform(const btMatrix3x3 &rotation_matrix, + const btVector3 &displacement, + const btVector3 &top_in, + const btVector3 &bottom_in, + btVector3 &top_out, + btVector3 &bottom_out) + { + top_out = rotation_matrix.transpose() * top_in; + bottom_out = rotation_matrix.transpose() * (bottom_in + displacement.cross(top_in)); + } + + btScalar SpatialDotProduct(const btVector3 &a_top, + const btVector3 &a_bottom, + const btVector3 &b_top, + const btVector3 &b_bottom) + { + return a_bottom.dot(b_top) + a_top.dot(b_bottom); + } +} + + +// +// Implementation of class btMultiBody +// + +btMultiBody::btMultiBody(int n_links, + btScalar mass, + const btVector3 &inertia, + bool fixed_base_, + bool can_sleep_) + : base_quat(0, 0, 0, 1), + base_mass(mass), + base_inertia(inertia), + + fixed_base(fixed_base_), + awake(true), + can_sleep(can_sleep_), + sleep_timer(0), + m_baseCollider(0), + m_linearDamping(0.04f), + m_angularDamping(0.04f), + m_useGyroTerm(true), + m_maxAppliedImpulse(1000.f), + m_hasSelfCollision(true) +{ + links.resize(n_links); + + vector_buf.resize(2*n_links); + matrix_buf.resize(n_links + 1); + m_real_buf.resize(6 + 2*n_links); + base_pos.setValue(0, 0, 0); + base_force.setValue(0, 0, 0); + base_torque.setValue(0, 0, 0); +} + +btMultiBody::~btMultiBody() +{ +} + +void btMultiBody::setupPrismatic(int i, + btScalar mass, + const btVector3 &inertia, + int parent, + const btQuaternion &rot_parent_to_this, + const btVector3 &joint_axis, + const btVector3 &r_vector_when_q_zero, + bool disableParentCollision) +{ + links[i].mass = mass; + links[i].inertia = inertia; + links[i].parent = parent; + links[i].zero_rot_parent_to_this = rot_parent_to_this; + links[i].axis_top.setValue(0,0,0); + links[i].axis_bottom = joint_axis; + links[i].e_vector = r_vector_when_q_zero; + links[i].is_revolute = false; + links[i].cached_rot_parent_to_this = rot_parent_to_this; + if (disableParentCollision) + links[i].m_flags |=BT_MULTIBODYLINKFLAGS_DISABLE_PARENT_COLLISION; + + links[i].updateCache(); +} + +void btMultiBody::setupRevolute(int i, + btScalar mass, + const btVector3 &inertia, + int parent, + const btQuaternion &zero_rot_parent_to_this, + const btVector3 &joint_axis, + const btVector3 &parent_axis_position, + const btVector3 &my_axis_position, + bool disableParentCollision) +{ + links[i].mass = mass; + links[i].inertia = inertia; + links[i].parent = parent; + links[i].zero_rot_parent_to_this = zero_rot_parent_to_this; + links[i].axis_top = joint_axis; + links[i].axis_bottom = joint_axis.cross(my_axis_position); + links[i].d_vector = my_axis_position; + links[i].e_vector = parent_axis_position; + links[i].is_revolute = true; + if (disableParentCollision) + links[i].m_flags |=BT_MULTIBODYLINKFLAGS_DISABLE_PARENT_COLLISION; + links[i].updateCache(); +} + + + + + +int btMultiBody::getParent(int i) const +{ + return links[i].parent; +} + +btScalar btMultiBody::getLinkMass(int i) const +{ + return links[i].mass; +} + +const btVector3 & btMultiBody::getLinkInertia(int i) const +{ + return links[i].inertia; +} + +btScalar btMultiBody::getJointPos(int i) const +{ + return links[i].joint_pos; +} + +btScalar btMultiBody::getJointVel(int i) const +{ + return m_real_buf[6 + i]; +} + +void btMultiBody::setJointPos(int i, btScalar q) +{ + links[i].joint_pos = q; + links[i].updateCache(); +} + +void btMultiBody::setJointVel(int i, btScalar qdot) +{ + m_real_buf[6 + i] = qdot; +} + +const btVector3 & btMultiBody::getRVector(int i) const +{ + return links[i].cached_r_vector; +} + +const btQuaternion & btMultiBody::getParentToLocalRot(int i) const +{ + return links[i].cached_rot_parent_to_this; +} + +btVector3 btMultiBody::localPosToWorld(int i, const btVector3 &local_pos) const +{ + btVector3 result = local_pos; + while (i != -1) { + // 'result' is in frame i. transform it to frame parent(i) + result += getRVector(i); + result = quatRotate(getParentToLocalRot(i).inverse(),result); + i = getParent(i); + } + + // 'result' is now in the base frame. transform it to world frame + result = quatRotate(getWorldToBaseRot().inverse() ,result); + result += getBasePos(); + + return result; +} + +btVector3 btMultiBody::worldPosToLocal(int i, const btVector3 &world_pos) const +{ + if (i == -1) { + // world to base + return quatRotate(getWorldToBaseRot(),(world_pos - getBasePos())); + } else { + // find position in parent frame, then transform to current frame + return quatRotate(getParentToLocalRot(i),worldPosToLocal(getParent(i), world_pos)) - getRVector(i); + } +} + +btVector3 btMultiBody::localDirToWorld(int i, const btVector3 &local_dir) const +{ + btVector3 result = local_dir; + while (i != -1) { + result = quatRotate(getParentToLocalRot(i).inverse() , result); + i = getParent(i); + } + result = quatRotate(getWorldToBaseRot().inverse() , result); + return result; +} + +btVector3 btMultiBody::worldDirToLocal(int i, const btVector3 &world_dir) const +{ + if (i == -1) { + return quatRotate(getWorldToBaseRot(), world_dir); + } else { + return quatRotate(getParentToLocalRot(i) ,worldDirToLocal(getParent(i), world_dir)); + } +} + +void btMultiBody::compTreeLinkVelocities(btVector3 *omega, btVector3 *vel) const +{ + int num_links = getNumLinks(); + // Calculates the velocities of each link (and the base) in its local frame + omega[0] = quatRotate(base_quat ,getBaseOmega()); + vel[0] = quatRotate(base_quat ,getBaseVel()); + + for (int i = 0; i < num_links; ++i) { + const int parent = links[i].parent; + + // transform parent vel into this frame, store in omega[i+1], vel[i+1] + SpatialTransform(btMatrix3x3(links[i].cached_rot_parent_to_this), links[i].cached_r_vector, + omega[parent+1], vel[parent+1], + omega[i+1], vel[i+1]); + + // now add qidot * shat_i + omega[i+1] += getJointVel(i) * links[i].axis_top; + vel[i+1] += getJointVel(i) * links[i].axis_bottom; + } +} + +btScalar btMultiBody::getKineticEnergy() const +{ + int num_links = getNumLinks(); + // TODO: would be better not to allocate memory here + btAlignedObjectArray<btVector3> omega;omega.resize(num_links+1); + btAlignedObjectArray<btVector3> vel;vel.resize(num_links+1); + compTreeLinkVelocities(&omega[0], &vel[0]); + + // we will do the factor of 0.5 at the end + btScalar result = base_mass * vel[0].dot(vel[0]); + result += omega[0].dot(base_inertia * omega[0]); + + for (int i = 0; i < num_links; ++i) { + result += links[i].mass * vel[i+1].dot(vel[i+1]); + result += omega[i+1].dot(links[i].inertia * omega[i+1]); + } + + return 0.5f * result; +} + +btVector3 btMultiBody::getAngularMomentum() const +{ + int num_links = getNumLinks(); + // TODO: would be better not to allocate memory here + btAlignedObjectArray<btVector3> omega;omega.resize(num_links+1); + btAlignedObjectArray<btVector3> vel;vel.resize(num_links+1); + btAlignedObjectArray<btQuaternion> rot_from_world;rot_from_world.resize(num_links+1); + compTreeLinkVelocities(&omega[0], &vel[0]); + + rot_from_world[0] = base_quat; + btVector3 result = quatRotate(rot_from_world[0].inverse() , (base_inertia * omega[0])); + + for (int i = 0; i < num_links; ++i) { + rot_from_world[i+1] = links[i].cached_rot_parent_to_this * rot_from_world[links[i].parent+1]; + result += (quatRotate(rot_from_world[i+1].inverse() , (links[i].inertia * omega[i+1]))); + } + + return result; +} + + +void btMultiBody::clearForcesAndTorques() +{ + base_force.setValue(0, 0, 0); + base_torque.setValue(0, 0, 0); + + for (int i = 0; i < getNumLinks(); ++i) { + links[i].applied_force.setValue(0, 0, 0); + links[i].applied_torque.setValue(0, 0, 0); + links[i].joint_torque = 0; + } +} + +void btMultiBody::clearVelocities() +{ + for (int i = 0; i < 6 + getNumLinks(); ++i) + { + m_real_buf[i] = 0.f; + } +} +void btMultiBody::addLinkForce(int i, const btVector3 &f) +{ + links[i].applied_force += f; +} + +void btMultiBody::addLinkTorque(int i, const btVector3 &t) +{ + links[i].applied_torque += t; +} + +void btMultiBody::addJointTorque(int i, btScalar Q) +{ + links[i].joint_torque += Q; +} + +const btVector3 & btMultiBody::getLinkForce(int i) const +{ + return links[i].applied_force; +} + +const btVector3 & btMultiBody::getLinkTorque(int i) const +{ + return links[i].applied_torque; +} + +btScalar btMultiBody::getJointTorque(int i) const +{ + return links[i].joint_torque; +} + + +inline btMatrix3x3 vecMulVecTranspose(const btVector3& v0, const btVector3& v1Transposed) +{ + btVector3 row0 = btVector3( + v0.x() * v1Transposed.x(), + v0.x() * v1Transposed.y(), + v0.x() * v1Transposed.z()); + btVector3 row1 = btVector3( + v0.y() * v1Transposed.x(), + v0.y() * v1Transposed.y(), + v0.y() * v1Transposed.z()); + btVector3 row2 = btVector3( + v0.z() * v1Transposed.x(), + v0.z() * v1Transposed.y(), + v0.z() * v1Transposed.z()); + + btMatrix3x3 m(row0[0],row0[1],row0[2], + row1[0],row1[1],row1[2], + row2[0],row2[1],row2[2]); + return m; +} + + +void btMultiBody::stepVelocities(btScalar dt, + btAlignedObjectArray<btScalar> &scratch_r, + btAlignedObjectArray<btVector3> &scratch_v, + btAlignedObjectArray<btMatrix3x3> &scratch_m) +{ + // Implement Featherstone's algorithm to calculate joint accelerations (q_double_dot) + // and the base linear & angular accelerations. + + // We apply damping forces in this routine as well as any external forces specified by the + // caller (via addBaseForce etc). + + // output should point to an array of 6 + num_links reals. + // Format is: 3 angular accelerations (in world frame), 3 linear accelerations (in world frame), + // num_links joint acceleration values. + + int num_links = getNumLinks(); + + const btScalar DAMPING_K1_LINEAR = m_linearDamping; + const btScalar DAMPING_K2_LINEAR = m_linearDamping; + + const btScalar DAMPING_K1_ANGULAR = m_angularDamping; + const btScalar DAMPING_K2_ANGULAR= m_angularDamping; + + btVector3 base_vel = getBaseVel(); + btVector3 base_omega = getBaseOmega(); + + // Temporary matrices/vectors -- use scratch space from caller + // so that we don't have to keep reallocating every frame + + scratch_r.resize(2*num_links + 6); + scratch_v.resize(8*num_links + 6); + scratch_m.resize(4*num_links + 4); + + btScalar * r_ptr = &scratch_r[0]; + btScalar * output = &scratch_r[num_links]; // "output" holds the q_double_dot results + btVector3 * v_ptr = &scratch_v[0]; + + // vhat_i (top = angular, bottom = linear part) + btVector3 * vel_top_angular = v_ptr; v_ptr += num_links + 1; + btVector3 * vel_bottom_linear = v_ptr; v_ptr += num_links + 1; + + // zhat_i^A + btVector3 * zero_acc_top_angular = v_ptr; v_ptr += num_links + 1; + btVector3 * zero_acc_bottom_linear = v_ptr; v_ptr += num_links + 1; + + // chat_i (note NOT defined for the base) + btVector3 * coriolis_top_angular = v_ptr; v_ptr += num_links; + btVector3 * coriolis_bottom_linear = v_ptr; v_ptr += num_links; + + // top left, top right and bottom left blocks of Ihat_i^A. + // bottom right block = transpose of top left block and is not stored. + // Note: the top right and bottom left blocks are always symmetric matrices, but we don't make use of this fact currently. + btMatrix3x3 * inertia_top_left = &scratch_m[num_links + 1]; + btMatrix3x3 * inertia_top_right = &scratch_m[2*num_links + 2]; + btMatrix3x3 * inertia_bottom_left = &scratch_m[3*num_links + 3]; + + // Cached 3x3 rotation matrices from parent frame to this frame. + btMatrix3x3 * rot_from_parent = &matrix_buf[0]; + btMatrix3x3 * rot_from_world = &scratch_m[0]; + + // hhat_i, ahat_i + // hhat is NOT stored for the base (but ahat is) + btVector3 * h_top = num_links > 0 ? &vector_buf[0] : 0; + btVector3 * h_bottom = num_links > 0 ? &vector_buf[num_links] : 0; + btVector3 * accel_top = v_ptr; v_ptr += num_links + 1; + btVector3 * accel_bottom = v_ptr; v_ptr += num_links + 1; + + // Y_i, D_i + btScalar * Y = r_ptr; r_ptr += num_links; + btScalar * D = num_links > 0 ? &m_real_buf[6 + num_links] : 0; + + // ptr to the joint accel part of the output + btScalar * joint_accel = output + 6; + + + // Start of the algorithm proper. + + // First 'upward' loop. + // Combines CompTreeLinkVelocities and InitTreeLinks from Mirtich. + + rot_from_parent[0] = btMatrix3x3(base_quat); + + vel_top_angular[0] = rot_from_parent[0] * base_omega; + vel_bottom_linear[0] = rot_from_parent[0] * base_vel; + + if (fixed_base) { + zero_acc_top_angular[0] = zero_acc_bottom_linear[0] = btVector3(0,0,0); + } else { + zero_acc_top_angular[0] = - (rot_from_parent[0] * (base_force + - base_mass*(DAMPING_K1_LINEAR+DAMPING_K2_LINEAR*base_vel.norm())*base_vel)); + + zero_acc_bottom_linear[0] = + - (rot_from_parent[0] * base_torque); + + if (m_useGyroTerm) + zero_acc_bottom_linear[0]+=vel_top_angular[0].cross( base_inertia * vel_top_angular[0] ); + + zero_acc_bottom_linear[0] += base_inertia * vel_top_angular[0] * (DAMPING_K1_ANGULAR + DAMPING_K2_ANGULAR*vel_top_angular[0].norm()); + + } + + + + inertia_top_left[0] = btMatrix3x3(0,0,0,0,0,0,0,0,0);//::Zero(); + + + inertia_top_right[0].setValue(base_mass, 0, 0, + 0, base_mass, 0, + 0, 0, base_mass); + inertia_bottom_left[0].setValue(base_inertia[0], 0, 0, + 0, base_inertia[1], 0, + 0, 0, base_inertia[2]); + + rot_from_world[0] = rot_from_parent[0]; + + for (int i = 0; i < num_links; ++i) { + const int parent = links[i].parent; + rot_from_parent[i+1] = btMatrix3x3(links[i].cached_rot_parent_to_this); + + + rot_from_world[i+1] = rot_from_parent[i+1] * rot_from_world[parent+1]; + + // vhat_i = i_xhat_p(i) * vhat_p(i) + SpatialTransform(rot_from_parent[i+1], links[i].cached_r_vector, + vel_top_angular[parent+1], vel_bottom_linear[parent+1], + vel_top_angular[i+1], vel_bottom_linear[i+1]); + + // we can now calculate chat_i + // remember vhat_i is really vhat_p(i) (but in current frame) at this point + coriolis_bottom_linear[i] = vel_top_angular[i+1].cross(vel_top_angular[i+1].cross(links[i].cached_r_vector)) + + 2 * vel_top_angular[i+1].cross(links[i].axis_bottom) * getJointVel(i); + if (links[i].is_revolute) { + coriolis_top_angular[i] = vel_top_angular[i+1].cross(links[i].axis_top) * getJointVel(i); + coriolis_bottom_linear[i] += (getJointVel(i) * getJointVel(i)) * links[i].axis_top.cross(links[i].axis_bottom); + } else { + coriolis_top_angular[i] = btVector3(0,0,0); + } + + // now set vhat_i to its true value by doing + // vhat_i += qidot * shat_i + vel_top_angular[i+1] += getJointVel(i) * links[i].axis_top; + vel_bottom_linear[i+1] += getJointVel(i) * links[i].axis_bottom; + + // calculate zhat_i^A + zero_acc_top_angular[i+1] = - (rot_from_world[i+1] * (links[i].applied_force)); + zero_acc_top_angular[i+1] += links[i].mass * (DAMPING_K1_LINEAR + DAMPING_K2_LINEAR*vel_bottom_linear[i+1].norm()) * vel_bottom_linear[i+1]; + + zero_acc_bottom_linear[i+1] = + - (rot_from_world[i+1] * links[i].applied_torque); + if (m_useGyroTerm) + { + zero_acc_bottom_linear[i+1] += vel_top_angular[i+1].cross( links[i].inertia * vel_top_angular[i+1] ); + } + + zero_acc_bottom_linear[i+1] += links[i].inertia * vel_top_angular[i+1] * (DAMPING_K1_ANGULAR + DAMPING_K2_ANGULAR*vel_top_angular[i+1].norm()); + + // calculate Ihat_i^A + inertia_top_left[i+1] = btMatrix3x3(0,0,0,0,0,0,0,0,0);//::Zero(); + inertia_top_right[i+1].setValue(links[i].mass, 0, 0, + 0, links[i].mass, 0, + 0, 0, links[i].mass); + inertia_bottom_left[i+1].setValue(links[i].inertia[0], 0, 0, + 0, links[i].inertia[1], 0, + 0, 0, links[i].inertia[2]); + } + + + // 'Downward' loop. + // (part of TreeForwardDynamics in Mirtich.) + for (int i = num_links - 1; i >= 0; --i) { + + h_top[i] = inertia_top_left[i+1] * links[i].axis_top + inertia_top_right[i+1] * links[i].axis_bottom; + h_bottom[i] = inertia_bottom_left[i+1] * links[i].axis_top + inertia_top_left[i+1].transpose() * links[i].axis_bottom; + btScalar val = SpatialDotProduct(links[i].axis_top, links[i].axis_bottom, h_top[i], h_bottom[i]); + D[i] = val; + Y[i] = links[i].joint_torque + - SpatialDotProduct(links[i].axis_top, links[i].axis_bottom, zero_acc_top_angular[i+1], zero_acc_bottom_linear[i+1]) + - SpatialDotProduct(h_top[i], h_bottom[i], coriolis_top_angular[i], coriolis_bottom_linear[i]); + + const int parent = links[i].parent; + + + // Ip += pXi * (Ii - hi hi' / Di) * iXp + const btScalar one_over_di = 1.0f / D[i]; + + + + + const btMatrix3x3 TL = inertia_top_left[i+1] - vecMulVecTranspose(one_over_di * h_top[i] , h_bottom[i]); + const btMatrix3x3 TR = inertia_top_right[i+1] - vecMulVecTranspose(one_over_di * h_top[i] , h_top[i]); + const btMatrix3x3 BL = inertia_bottom_left[i+1]- vecMulVecTranspose(one_over_di * h_bottom[i] , h_bottom[i]); + + + btMatrix3x3 r_cross; + r_cross.setValue( + 0, -links[i].cached_r_vector[2], links[i].cached_r_vector[1], + links[i].cached_r_vector[2], 0, -links[i].cached_r_vector[0], + -links[i].cached_r_vector[1], links[i].cached_r_vector[0], 0); + + inertia_top_left[parent+1] += rot_from_parent[i+1].transpose() * ( TL - TR * r_cross ) * rot_from_parent[i+1]; + inertia_top_right[parent+1] += rot_from_parent[i+1].transpose() * TR * rot_from_parent[i+1]; + inertia_bottom_left[parent+1] += rot_from_parent[i+1].transpose() * + (r_cross * (TL - TR * r_cross) + BL - TL.transpose() * r_cross) * rot_from_parent[i+1]; + + + // Zp += pXi * (Zi + Ii*ci + hi*Yi/Di) + btVector3 in_top, in_bottom, out_top, out_bottom; + const btScalar Y_over_D = Y[i] * one_over_di; + in_top = zero_acc_top_angular[i+1] + + inertia_top_left[i+1] * coriolis_top_angular[i] + + inertia_top_right[i+1] * coriolis_bottom_linear[i] + + Y_over_D * h_top[i]; + in_bottom = zero_acc_bottom_linear[i+1] + + inertia_bottom_left[i+1] * coriolis_top_angular[i] + + inertia_top_left[i+1].transpose() * coriolis_bottom_linear[i] + + Y_over_D * h_bottom[i]; + InverseSpatialTransform(rot_from_parent[i+1], links[i].cached_r_vector, + in_top, in_bottom, out_top, out_bottom); + zero_acc_top_angular[parent+1] += out_top; + zero_acc_bottom_linear[parent+1] += out_bottom; + } + + + // Second 'upward' loop + // (part of TreeForwardDynamics in Mirtich) + + if (fixed_base) + { + accel_top[0] = accel_bottom[0] = btVector3(0,0,0); + } + else + { + if (num_links > 0) + { + //Matrix<btScalar, 6, 6> Imatrix; + //Imatrix.block<3,3>(0,0) = inertia_top_left[0]; + //Imatrix.block<3,3>(3,0) = inertia_bottom_left[0]; + //Imatrix.block<3,3>(0,3) = inertia_top_right[0]; + //Imatrix.block<3,3>(3,3) = inertia_top_left[0].transpose(); + //cached_imatrix_lu.reset(new Eigen::LU<Matrix<btScalar, 6, 6> >(Imatrix)); // TODO: Avoid memory allocation here? + + cached_inertia_top_left = inertia_top_left[0]; + cached_inertia_top_right = inertia_top_right[0]; + cached_inertia_lower_left = inertia_bottom_left[0]; + cached_inertia_lower_right= inertia_top_left[0].transpose(); + + } + btVector3 rhs_top (zero_acc_top_angular[0][0], zero_acc_top_angular[0][1], zero_acc_top_angular[0][2]); + btVector3 rhs_bot (zero_acc_bottom_linear[0][0], zero_acc_bottom_linear[0][1], zero_acc_bottom_linear[0][2]); + float result[6]; + + solveImatrix(rhs_top, rhs_bot, result); +// printf("result=%f,%f,%f,%f,%f,%f\n",result[0],result[0],result[0],result[0],result[0],result[0]); + for (int i = 0; i < 3; ++i) { + accel_top[0][i] = -result[i]; + accel_bottom[0][i] = -result[i+3]; + } + + } + + // now do the loop over the links + for (int i = 0; i < num_links; ++i) { + const int parent = links[i].parent; + SpatialTransform(rot_from_parent[i+1], links[i].cached_r_vector, + accel_top[parent+1], accel_bottom[parent+1], + accel_top[i+1], accel_bottom[i+1]); + joint_accel[i] = (Y[i] - SpatialDotProduct(h_top[i], h_bottom[i], accel_top[i+1], accel_bottom[i+1])) / D[i]; + accel_top[i+1] += coriolis_top_angular[i] + joint_accel[i] * links[i].axis_top; + accel_bottom[i+1] += coriolis_bottom_linear[i] + joint_accel[i] * links[i].axis_bottom; + } + + // transform base accelerations back to the world frame. + btVector3 omegadot_out = rot_from_parent[0].transpose() * accel_top[0]; + output[0] = omegadot_out[0]; + output[1] = omegadot_out[1]; + output[2] = omegadot_out[2]; + + btVector3 vdot_out = rot_from_parent[0].transpose() * accel_bottom[0]; + output[3] = vdot_out[0]; + output[4] = vdot_out[1]; + output[5] = vdot_out[2]; + // Final step: add the accelerations (times dt) to the velocities. + applyDeltaVee(output, dt); + + +} + + + +void btMultiBody::solveImatrix(const btVector3& rhs_top, const btVector3& rhs_bot, float result[6]) const +{ + int num_links = getNumLinks(); + ///solve I * x = rhs, so the result = invI * rhs + if (num_links == 0) + { + // in the case of 0 links (i.e. a plain rigid body, not a multibody) rhs * invI is easier + result[0] = rhs_bot[0] / base_inertia[0]; + result[1] = rhs_bot[1] / base_inertia[1]; + result[2] = rhs_bot[2] / base_inertia[2]; + result[3] = rhs_top[0] / base_mass; + result[4] = rhs_top[1] / base_mass; + result[5] = rhs_top[2] / base_mass; + } else + { + /// Special routine for calculating the inverse of a spatial inertia matrix + ///the 6x6 matrix is stored as 4 blocks of 3x3 matrices + btMatrix3x3 Binv = cached_inertia_top_right.inverse()*-1.f; + btMatrix3x3 tmp = cached_inertia_lower_right * Binv; + btMatrix3x3 invIupper_right = (tmp * cached_inertia_top_left + cached_inertia_lower_left).inverse(); + tmp = invIupper_right * cached_inertia_lower_right; + btMatrix3x3 invI_upper_left = (tmp * Binv); + btMatrix3x3 invI_lower_right = (invI_upper_left).transpose(); + tmp = cached_inertia_top_left * invI_upper_left; + tmp[0][0]-= 1.0; + tmp[1][1]-= 1.0; + tmp[2][2]-= 1.0; + btMatrix3x3 invI_lower_left = (Binv * tmp); + + //multiply result = invI * rhs + { + btVector3 vtop = invI_upper_left*rhs_top; + btVector3 tmp; + tmp = invIupper_right * rhs_bot; + vtop += tmp; + btVector3 vbot = invI_lower_left*rhs_top; + tmp = invI_lower_right * rhs_bot; + vbot += tmp; + result[0] = vtop[0]; + result[1] = vtop[1]; + result[2] = vtop[2]; + result[3] = vbot[0]; + result[4] = vbot[1]; + result[5] = vbot[2]; + } + + } +} + + +void btMultiBody::calcAccelerationDeltas(const btScalar *force, btScalar *output, + btAlignedObjectArray<btScalar> &scratch_r, btAlignedObjectArray<btVector3> &scratch_v) const +{ + // Temporary matrices/vectors -- use scratch space from caller + // so that we don't have to keep reallocating every frame + int num_links = getNumLinks(); + scratch_r.resize(num_links); + scratch_v.resize(4*num_links + 4); + + btScalar * r_ptr = num_links == 0 ? 0 : &scratch_r[0]; + btVector3 * v_ptr = &scratch_v[0]; + + // zhat_i^A (scratch space) + btVector3 * zero_acc_top_angular = v_ptr; v_ptr += num_links + 1; + btVector3 * zero_acc_bottom_linear = v_ptr; v_ptr += num_links + 1; + + // rot_from_parent (cached from calcAccelerations) + const btMatrix3x3 * rot_from_parent = &matrix_buf[0]; + + // hhat (cached), accel (scratch) + const btVector3 * h_top = num_links > 0 ? &vector_buf[0] : 0; + const btVector3 * h_bottom = num_links > 0 ? &vector_buf[num_links] : 0; + btVector3 * accel_top = v_ptr; v_ptr += num_links + 1; + btVector3 * accel_bottom = v_ptr; v_ptr += num_links + 1; + + // Y_i (scratch), D_i (cached) + btScalar * Y = r_ptr; r_ptr += num_links; + const btScalar * D = num_links > 0 ? &m_real_buf[6 + num_links] : 0; + + btAssert(num_links == 0 || r_ptr - &scratch_r[0] == scratch_r.size()); + btAssert(v_ptr - &scratch_v[0] == scratch_v.size()); + + + + // First 'upward' loop. + // Combines CompTreeLinkVelocities and InitTreeLinks from Mirtich. + + btVector3 input_force(force[3],force[4],force[5]); + btVector3 input_torque(force[0],force[1],force[2]); + + // Fill in zero_acc + // -- set to force/torque on the base, zero otherwise + if (fixed_base) + { + zero_acc_top_angular[0] = zero_acc_bottom_linear[0] = btVector3(0,0,0); + } else + { + zero_acc_top_angular[0] = - (rot_from_parent[0] * input_force); + zero_acc_bottom_linear[0] = - (rot_from_parent[0] * input_torque); + } + for (int i = 0; i < num_links; ++i) + { + zero_acc_top_angular[i+1] = zero_acc_bottom_linear[i+1] = btVector3(0,0,0); + } + + // 'Downward' loop. + for (int i = num_links - 1; i >= 0; --i) + { + + Y[i] = - SpatialDotProduct(links[i].axis_top, links[i].axis_bottom, zero_acc_top_angular[i+1], zero_acc_bottom_linear[i+1]); + Y[i] += force[6 + i]; // add joint torque + + const int parent = links[i].parent; + + // Zp += pXi * (Zi + hi*Yi/Di) + btVector3 in_top, in_bottom, out_top, out_bottom; + const btScalar Y_over_D = Y[i] / D[i]; + in_top = zero_acc_top_angular[i+1] + Y_over_D * h_top[i]; + in_bottom = zero_acc_bottom_linear[i+1] + Y_over_D * h_bottom[i]; + InverseSpatialTransform(rot_from_parent[i+1], links[i].cached_r_vector, + in_top, in_bottom, out_top, out_bottom); + zero_acc_top_angular[parent+1] += out_top; + zero_acc_bottom_linear[parent+1] += out_bottom; + } + + // ptr to the joint accel part of the output + btScalar * joint_accel = output + 6; + + // Second 'upward' loop + if (fixed_base) + { + accel_top[0] = accel_bottom[0] = btVector3(0,0,0); + } else + { + btVector3 rhs_top (zero_acc_top_angular[0][0], zero_acc_top_angular[0][1], zero_acc_top_angular[0][2]); + btVector3 rhs_bot (zero_acc_bottom_linear[0][0], zero_acc_bottom_linear[0][1], zero_acc_bottom_linear[0][2]); + + float result[6]; + solveImatrix(rhs_top,rhs_bot, result); + // printf("result=%f,%f,%f,%f,%f,%f\n",result[0],result[0],result[0],result[0],result[0],result[0]); + + for (int i = 0; i < 3; ++i) { + accel_top[0][i] = -result[i]; + accel_bottom[0][i] = -result[i+3]; + } + + } + + // now do the loop over the links + for (int i = 0; i < num_links; ++i) { + const int parent = links[i].parent; + SpatialTransform(rot_from_parent[i+1], links[i].cached_r_vector, + accel_top[parent+1], accel_bottom[parent+1], + accel_top[i+1], accel_bottom[i+1]); + joint_accel[i] = (Y[i] - SpatialDotProduct(h_top[i], h_bottom[i], accel_top[i+1], accel_bottom[i+1])) / D[i]; + accel_top[i+1] += joint_accel[i] * links[i].axis_top; + accel_bottom[i+1] += joint_accel[i] * links[i].axis_bottom; + } + + // transform base accelerations back to the world frame. + btVector3 omegadot_out; + omegadot_out = rot_from_parent[0].transpose() * accel_top[0]; + output[0] = omegadot_out[0]; + output[1] = omegadot_out[1]; + output[2] = omegadot_out[2]; + + btVector3 vdot_out; + vdot_out = rot_from_parent[0].transpose() * accel_bottom[0]; + + output[3] = vdot_out[0]; + output[4] = vdot_out[1]; + output[5] = vdot_out[2]; +} + +void btMultiBody::stepPositions(btScalar dt) +{ + int num_links = getNumLinks(); + // step position by adding dt * velocity + btVector3 v = getBaseVel(); + base_pos += dt * v; + + // "exponential map" method for the rotation + btVector3 base_omega = getBaseOmega(); + const btScalar omega_norm = base_omega.norm(); + const btScalar omega_times_dt = omega_norm * dt; + const btScalar SMALL_ROTATION_ANGLE = 0.02f; // Theoretically this should be ~ pow(FLT_EPSILON,0.25) which is ~ 0.0156 + if (fabs(omega_times_dt) < SMALL_ROTATION_ANGLE) + { + const btScalar xsq = omega_times_dt * omega_times_dt; // |omega|^2 * dt^2 + const btScalar sin_term = dt * (xsq / 48.0f - 0.5f); // -sin(0.5*dt*|omega|) / |omega| + const btScalar cos_term = 1.0f - xsq / 8.0f; // cos(0.5*dt*|omega|) + base_quat = base_quat * btQuaternion(sin_term * base_omega[0],sin_term * base_omega[1],sin_term * base_omega[2],cos_term); + } else + { + base_quat = base_quat * btQuaternion(base_omega / omega_norm,-omega_times_dt); + } + + // Make sure the quaternion represents a valid rotation. + // (Not strictly necessary, but helps prevent any round-off errors from building up.) + base_quat.normalize(); + + // Finally we can update joint_pos for each of the links + for (int i = 0; i < num_links; ++i) + { + float jointVel = getJointVel(i); + links[i].joint_pos += dt * jointVel; + links[i].updateCache(); + } +} + +void btMultiBody::fillContactJacobian(int link, + const btVector3 &contact_point, + const btVector3 &normal, + btScalar *jac, + btAlignedObjectArray<btScalar> &scratch_r, + btAlignedObjectArray<btVector3> &scratch_v, + btAlignedObjectArray<btMatrix3x3> &scratch_m) const +{ + // temporary space + int num_links = getNumLinks(); + scratch_v.resize(2*num_links + 2); + scratch_m.resize(num_links + 1); + + btVector3 * v_ptr = &scratch_v[0]; + btVector3 * p_minus_com = v_ptr; v_ptr += num_links + 1; + btVector3 * n_local = v_ptr; v_ptr += num_links + 1; + btAssert(v_ptr - &scratch_v[0] == scratch_v.size()); + + scratch_r.resize(num_links); + btScalar * results = num_links > 0 ? &scratch_r[0] : 0; + + btMatrix3x3 * rot_from_world = &scratch_m[0]; + + const btVector3 p_minus_com_world = contact_point - base_pos; + + rot_from_world[0] = btMatrix3x3(base_quat); + + p_minus_com[0] = rot_from_world[0] * p_minus_com_world; + n_local[0] = rot_from_world[0] * normal; + + // omega coeffients first. + btVector3 omega_coeffs; + omega_coeffs = p_minus_com_world.cross(normal); + jac[0] = omega_coeffs[0]; + jac[1] = omega_coeffs[1]; + jac[2] = omega_coeffs[2]; + // then v coefficients + jac[3] = normal[0]; + jac[4] = normal[1]; + jac[5] = normal[2]; + + // Set remaining jac values to zero for now. + for (int i = 6; i < 6 + num_links; ++i) { + jac[i] = 0; + } + + // Qdot coefficients, if necessary. + if (num_links > 0 && link > -1) { + + // TODO: speed this up -- don't calculate for links we don't need. + // (Also, we are making 3 separate calls to this function, for the normal & the 2 friction directions, + // which is resulting in repeated work being done...) + + // calculate required normals & positions in the local frames. + for (int i = 0; i < num_links; ++i) { + + // transform to local frame + const int parent = links[i].parent; + const btMatrix3x3 mtx(links[i].cached_rot_parent_to_this); + rot_from_world[i+1] = mtx * rot_from_world[parent+1]; + + n_local[i+1] = mtx * n_local[parent+1]; + p_minus_com[i+1] = mtx * p_minus_com[parent+1] - links[i].cached_r_vector; + + // calculate the jacobian entry + if (links[i].is_revolute) { + results[i] = n_local[i+1].dot( links[i].axis_top.cross(p_minus_com[i+1]) + links[i].axis_bottom ); + } else { + results[i] = n_local[i+1].dot( links[i].axis_bottom ); + } + } + + // Now copy through to output. + while (link != -1) { + jac[6 + link] = results[link]; + link = links[link].parent; + } + } +} + +void btMultiBody::wakeUp() +{ + awake = true; +} + +void btMultiBody::goToSleep() +{ + awake = false; +} + +void btMultiBody::checkMotionAndSleepIfRequired(btScalar timestep) +{ + int num_links = getNumLinks(); + extern bool gDisableDeactivation; + if (!can_sleep || gDisableDeactivation) + { + awake = true; + sleep_timer = 0; + return; + } + + // motion is computed as omega^2 + v^2 + (sum of squares of joint velocities) + btScalar motion = 0; + for (int i = 0; i < 6 + num_links; ++i) { + motion += m_real_buf[i] * m_real_buf[i]; + } + + if (motion < SLEEP_EPSILON) { + sleep_timer += timestep; + if (sleep_timer > SLEEP_TIMEOUT) { + goToSleep(); + } + } else { + sleep_timer = 0; + if (!awake) + wakeUp(); + } +} |