IK_QJacobianSolver.cpp

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/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#include <algorithm>
#include <cstdio>
 
#include "IK_QJacobianSolver.h"
 
// #include "analyze.h"
IK_QJacobianSolver::IK_QJacobianSolver()
{
  m_poleconstraint = false;
  m_getpoleangle = false;
  m_rootmatrix.setIdentity();
}
 
double IK_QJacobianSolver::ComputeScale()
{
  std::vector<IK_QSegment *>::iterator seg;
  double length = 0.0f;
 
  for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
    length += (*seg)->MaxExtension();
  }
 
  if (length == 0.0) {
    return 1.0;
  }
  return 1.0 / length;
}
 
void IK_QJacobianSolver::Scale(double scale, std::list<IK_QTask *> &tasks)
{
  std::list<IK_QTask *>::iterator task;
  std::vector<IK_QSegment *>::iterator seg;
 
  for (task = tasks.begin(); task != tasks.end(); task++) {
    (*task)->Scale(scale);
  }
 
  for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
    (*seg)->Scale(scale);
  }
 
  m_rootmatrix.translation() *= scale;
  m_goal *= scale;
  m_polegoal *= scale;
}
 
void IK_QJacobianSolver::AddSegmentList(IK_QSegment *seg)
{
  m_segments.push_back(seg);
 
  IK_QSegment *child;
  for (child = seg->Child(); child; child = child->Sibling()) {
    AddSegmentList(child);
  }
}
 
bool IK_QJacobianSolver::Setup(IK_QSegment *root, std::list<IK_QTask *> &tasks)
{
  m_segments.clear();
  AddSegmentList(root);
 
  // assign each segment a unique id for the jacobian
  std::vector<IK_QSegment *>::iterator seg;
  int num_dof = 0;
 
  for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
    (*seg)->SetDoFId(num_dof);
    num_dof += (*seg)->NumberOfDoF();
  }
 
  if (num_dof == 0) {
    return false;
  }
 
  // compute task ids and assign weights to task
  int primary_size = 0;
  int secondary_size = 0, secondary = 0;
  double primary_weight = 0.0, secondary_weight = 0.0;
  std::list<IK_QTask *>::iterator task;
 
  for (task = tasks.begin(); task != tasks.end(); task++) {
    IK_QTask *qtask = *task;
 
    if (qtask->Primary()) {
      qtask->SetId(primary_size);
      primary_size += qtask->Size();
      primary_weight += qtask->Weight();
    }
    else {
      qtask->SetId(secondary_size);
      secondary_size += qtask->Size();
      secondary_weight += qtask->Weight();
      secondary++;
    }
  }
 
  if (primary_size == 0 || FuzzyZero(primary_weight)) {
    return false;
  }
 
  m_secondary_enabled = (secondary > 0);
 
  // rescale weights of tasks to sum up to 1
  double primary_rescale = 1.0 / primary_weight;
  double secondary_rescale;
  if (FuzzyZero(secondary_weight)) {
    secondary_rescale = 0.0;
  }
  else {
    secondary_rescale = 1.0 / secondary_weight;
  }
 
  for (task = tasks.begin(); task != tasks.end(); task++) {
    IK_QTask *qtask = *task;
 
    if (qtask->Primary()) {
      qtask->SetWeight(qtask->Weight() * primary_rescale);
    }
    else {
      qtask->SetWeight(qtask->Weight() * secondary_rescale);
    }
  }
 
  // set matrix sizes
  m_jacobian.ArmMatrices(num_dof, primary_size);
  if (secondary > 0) {
    m_jacobian_sub.ArmMatrices(num_dof, secondary_size);
  }
 
  // set dof weights
  int i;
 
  for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
    for (i = 0; i < (*seg)->NumberOfDoF(); i++) {
      m_jacobian.SetDoFWeight((*seg)->DoFId() + i, (*seg)->Weight(i));
    }
  }
 
  return true;
}
 
void IK_QJacobianSolver::SetPoleVectorConstraint(
    IK_QSegment *tip, Vector3d &goal, Vector3d &polegoal, float poleangle, bool getangle)
{
  m_poleconstraint = true;
  m_poletip = tip;
  m_goal = goal;
  m_polegoal = polegoal;
  m_poleangle = (getangle) ? 0.0f : poleangle;
  m_getpoleangle = getangle;
}
 
void IK_QJacobianSolver::ConstrainPoleVector(IK_QSegment *root, std::list<IK_QTask *> &tasks)
{
  // this function will be called before and after solving. calling it before
  // solving gives predictable solutions by rotating towards the solution,
  // and calling it afterwards ensures the solution is exact.
 
  if (!m_poleconstraint) {
    return;
  }
 
  // disable pole vector constraint in case of multiple position tasks
  std::list<IK_QTask *>::iterator task;
  int positiontasks = 0;
 
  for (task = tasks.begin(); task != tasks.end(); task++) {
    if ((*task)->PositionTask()) {
      positiontasks++;
    }
  }
 
  if (positiontasks >= 2) {
    m_poleconstraint = false;
    return;
  }
 
  // get positions and rotations
  root->UpdateTransform(m_rootmatrix);
 
  const Vector3d rootpos = root->GlobalStart();
  const Vector3d endpos = m_poletip->GlobalEnd();
  const Matrix3d &rootbasis = root->GlobalTransform().linear();
 
  // construct "lookat" matrices (like gluLookAt), based on a direction and
  // an up vector, with the direction going from the root to the end effector
  // and the up vector going from the root to the pole constraint position.
  Vector3d dir = normalize(endpos - rootpos);
  Vector3d rootx = rootbasis.col(0);
  Vector3d rootz = rootbasis.col(2);
  Vector3d up = rootx * cos(m_poleangle) + rootz * sin(m_poleangle);
 
  // in post, don't rotate towards the goal but only correct the pole up
  Vector3d poledir = (m_getpoleangle) ? dir : normalize(m_goal - rootpos);
  Vector3d poleup = normalize(m_polegoal - rootpos);
 
  Matrix3d mat, polemat;
 
  mat.row(0) = normalize(dir.cross(up));
  mat.row(1) = mat.row(0).cross(dir);
  mat.row(2) = -dir;
 
  polemat.row(0) = normalize(poledir.cross(poleup));
  polemat.row(1) = polemat.row(0).cross(poledir);
  polemat.row(2) = -poledir;
 
  if (m_getpoleangle) {
    // we compute the pole angle that to rotate towards the target
    m_poleangle = angle(mat.row(1), polemat.row(1));
 
    double dt = rootz.dot(mat.row(1) * cos(m_poleangle) + mat.row(0) * sin(m_poleangle));
    if (dt > 0.0) {
      m_poleangle = -m_poleangle;
    }
 
    // solve again, with the pole angle we just computed
    m_getpoleangle = false;
    ConstrainPoleVector(root, tasks);
  }
  else {
    // now we set as root matrix the difference between the current and
    // desired rotation based on the pole vector constraint. we use
    // transpose instead of inverse because we have orthogonal matrices
    // anyway, and in case of a singular matrix we don't get NaN's.
    Affine3d trans;
    trans.linear() = polemat.transpose() * mat;
    trans.translation() = Vector3d(0, 0, 0);
    m_rootmatrix = trans * m_rootmatrix;
  }
}
 
bool IK_QJacobianSolver::UpdateAngles(double &norm)
{
  // assign each segment a unique id for the jacobian
  std::vector<IK_QSegment *>::iterator seg;
  IK_QSegment *qseg, *minseg = nullptr;
  double minabsdelta = 1e10, absdelta;
  Vector3d delta, mindelta;
  bool locked = false, clamp[3];
  int i, mindof = 0;
 
  // here we check if any angle limits were violated. angles whose clamped
  // position is the same as it was before, are locked immediate. of the
  // other violation angles the most violating angle is rememberd
  for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
    qseg = *seg;
    if (qseg->UpdateAngle(m_jacobian, delta, clamp)) {
      for (i = 0; i < qseg->NumberOfDoF(); i++) {
        if (clamp[i] && !qseg->Locked(i)) {
          absdelta = fabs(delta[i]);
 
          if (absdelta < IK_EPSILON) {
            qseg->Lock(i, m_jacobian, delta);
            locked = true;
          }
          else if (absdelta < minabsdelta) {
            minabsdelta = absdelta;
            mindelta = delta;
            minseg = qseg;
            mindof = i;
          }
        }
      }
    }
  }
 
  // lock most violating angle
  if (minseg) {
    minseg->Lock(mindof, m_jacobian, mindelta);
    locked = true;
 
    norm = std::max(minabsdelta, norm);
  }
 
  if (locked == false) {
    // no locking done, last inner iteration, apply the angles
    for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
      (*seg)->UnLock();
      (*seg)->UpdateAngleApply();
    }
  }
 
  // signal if another inner iteration is needed
  return locked;
}
 
bool IK_QJacobianSolver::Solve(IK_QSegment *root,
                               std::list<IK_QTask *> tasks,
                               const double /*tolerance*/,
                               const int max_iterations)
{
  float scale = ComputeScale();
  bool solved = false;
  // double dt = analyze_time();
 
  Scale(scale, tasks);
 
  ConstrainPoleVector(root, tasks);
 
  root->UpdateTransform(m_rootmatrix);
 
  // iterate
  for (int iterations = 0; iterations < max_iterations; iterations++) {
    // update transform
    root->UpdateTransform(m_rootmatrix);
 
    std::list<IK_QTask *>::iterator task;
 
    // compute jacobian
    for (task = tasks.begin(); task != tasks.end(); task++) {
      if ((*task)->Primary()) {
        (*task)->ComputeJacobian(m_jacobian);
      }
      else {
        (*task)->ComputeJacobian(m_jacobian_sub);
      }
    }
 
    double norm = 0.0;
 
    do {
      // invert jacobian
      try {
        m_jacobian.Invert();
        if (m_secondary_enabled) {
          m_jacobian.SubTask(m_jacobian_sub);
        }
      }
      catch (...) {
        fprintf(stderr, "IK Exception\n");
        return false;
      }
 
      // update angles and check limits
    } while (UpdateAngles(norm));
 
    // unlock segments again after locking in clamping loop
    std::vector<IK_QSegment *>::iterator seg;
    for (seg = m_segments.begin(); seg != m_segments.end(); seg++) {
      (*seg)->UnLock();
    }
 
    // compute angle update norm
    double maxnorm = m_jacobian.AngleUpdateNorm();
    norm = std::max(maxnorm, norm);
 
    // check for convergence
    if (norm < 1e-3 && iterations > 10) {
      solved = true;
      break;
    }
  }
 
  if (m_poleconstraint) {
    root->PrependBasis(m_rootmatrix.linear());
  }
 
  Scale(1.0f / scale, tasks);
 
  // analyze_add_run(max_iterations, analyze_time()-dt);
 
  return solved;
}