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// Copyright (c) 2017 CNRS |
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// |
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// This file is part of tsid |
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// tsid is free software: you can redistribute it |
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// and/or modify it under the terms of the GNU Lesser General Public |
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// License as published by the Free Software Foundation, either version |
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// 3 of the License, or (at your option) any later version. |
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// tsid is distributed in the hope that it will be |
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// useful, but WITHOUT ANY WARRANTY; without even the implied warranty |
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// of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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// General Lesser Public License for more details. You should have |
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// received a copy of the GNU Lesser General Public License along with |
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// tsid If not, see |
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// <http://www.gnu.org/licenses/>. |
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// |
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#include <tsid/tasks/task-joint-posVelAcc-bounds.hpp> |
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#include "tsid/robots/robot-wrapper.hpp" |
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// #include <tsid/utils/stop-watch.hpp> |
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/** This class has been implemented following : |
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* Andrea del Prete. Joint Position and Velocity Bounds in Discrete-Time |
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* Acceleration/Torque Control of Robot Manipulators. IEEE Robotics and |
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* Automation Letters, IEEE 2018, 3 (1), |
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* pp.281-288.10.1109/LRA.2017.2738321. hal-01356989v3 And |
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* https://github.com/andreadelprete/pinocchio_inv_dyn/blob/master/python/pinocchio_inv_dyn/acc_bounds_util.py |
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*/ |
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namespace tsid { |
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namespace tasks { |
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using namespace math; |
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using namespace trajectories; |
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using namespace pinocchio; |
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TaskJointPosVelAccBounds::TaskJointPosVelAccBounds(const std::string& name, |
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RobotWrapper& robot, |
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double dt, bool verbose) |
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: TaskMotion(name, robot), |
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m_constraint(name, robot.na(), robot.nv()), |
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m_dt(2 * dt), |
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m_verbose(verbose), |
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m_nv(robot.nv()), |
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m_na(robot.na()) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT(dt > 0.0, "dt needs to be positive"); |
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m_eps = 1e-10; |
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m_qMin = Vector::Constant(m_na, 1, -1e10); |
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m_qMax = Vector::Constant(m_na, 1, 1e10); |
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m_dqMax = Vector::Constant(m_na, 1, 1e10); |
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m_ddqMax = Vector::Constant(m_na, 1, 1e10); |
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m_impose_position_bounds = false; |
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m_impose_velocity_bounds = false; |
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m_impose_viability_bounds = false; |
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m_impose_acceleration_bounds = false; |
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// Used in computeAccLimitsFromPosLimits |
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m_two_dt_sq = 2.0 / (m_dt * m_dt); |
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m_ddqMax_q3 = Vector::Zero(m_na); |
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m_ddqMin_q3 = Vector::Zero(m_na); |
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m_ddqMax_q2 = Vector::Zero(m_na); |
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m_ddqMin_q2 = Vector::Zero(m_na); |
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m_minus_dq_over_dt = Vector::Zero(m_na); |
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// Used in computeAccLimitsFromViability |
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m_dt_square = m_dt * m_dt; |
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m_two_a = 2 * m_dt_square; |
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m_dt_dq = Vector::Zero(m_na); |
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m_dt_two_dq = Vector::Zero(m_na); |
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m_two_ddqMax = Vector::Zero(m_na); |
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m_dt_ddqMax_dt = Vector::Zero(m_na); |
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m_dq_square = Vector::Zero(m_na); |
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m_q_plus_dt_dq = Vector::Zero(m_na); |
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m_b_1 = Vector::Zero(m_na); |
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m_b_2 = Vector::Zero(m_na); |
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m_ddq_1 = Vector::Zero(m_na); |
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m_ddq_2 = Vector::Zero(m_na); |
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m_c_1 = Vector::Zero(m_na); |
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m_delta_1 = Vector::Zero(m_na); |
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m_c_2 = Vector::Zero(m_na); |
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m_delta_2 = Vector::Zero(m_na); |
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// Used in computeAccLimits |
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m_ub = Vector::Constant(4, 1, 1e10); |
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m_lb = Vector::Constant(4, 1, -1e10); |
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m_ddqLBPos = Vector::Constant(m_na, 1, -1e10); |
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m_ddqUBPos = Vector::Constant(m_na, 1, 1e10); |
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m_ddqLBVia = Vector::Constant(m_na, 1, -1e10); |
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m_ddqUBVia = Vector::Constant(m_na, 1, 1e10); |
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m_ddqLBVel = Vector::Constant(m_na, 1, -1e10); |
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m_ddqUBVel = Vector::Constant(m_na, 1, 1e10); |
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m_ddqLBAcc = Vector::Constant(m_na, 1, -1e10); |
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m_ddqUBAcc = Vector::Constant(m_na, 1, 1e10); |
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m_ddqLB = Vector::Constant(m_na, 1, -1e10); |
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m_ddqUB = Vector::Constant(m_na, 1, 1e10); |
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m_viabViol = Vector::Zero(m_na); |
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m_qa = Vector::Zero(m_na); |
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m_dqa = Vector::Zero(m_na); |
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Vector m = Vector::Ones(robot.na()); |
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setMask(m); |
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for (int i = 0; i < m_na; i++) { |
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m_constraint.upperBound()(i) = 1e10; |
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m_constraint.lowerBound()(i) = -1e10; |
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} |
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} |
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const Vector& TaskJointPosVelAccBounds::mask() const { return m_mask; } |
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void TaskJointPosVelAccBounds::mask(const Vector& m) { |
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// std::cerr<<"The method TaskJointPosVelAccBounds::mask is deprecated. Use |
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// TaskJointPosVelAccBounds::setMask instead.\n"; |
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return setMask(m); |
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} |
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void TaskJointPosVelAccBounds::setMask(ConstRefVector m) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT(m.size() == m_robot.na(), |
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"The size of the mask vector needs to equal " + |
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std::to_string(m_robot.na())); |
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m_mask = m; |
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const Vector::Index dim = static_cast<Vector::Index>(m.sum()); |
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Matrix S = Matrix::Zero(dim, m_robot.nv()); |
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m_activeAxes.resize(dim); |
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unsigned int j = 0; |
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for (unsigned int i = 0; i < m.size(); i++) |
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if (m(i) != 0.0) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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m(i) == 1.0, "Mask entries need to be either 0.0 or 1.0"); |
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S(j, m_robot.nv() - m_robot.na() + i) = 1.0; |
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m_activeAxes(j) = i; |
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j++; |
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} |
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m_constraint.resize((unsigned int)dim, m_robot.nv()); |
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m_constraint.setMatrix(S); |
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} |
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int TaskJointPosVelAccBounds::dim() const { return m_na; } |
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const Vector& TaskJointPosVelAccBounds::getAccelerationBounds() const { |
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return m_ddqMax; |
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} |
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const Vector& TaskJointPosVelAccBounds::getVelocityBounds() const { |
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return m_dqMax; |
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} |
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const Vector& TaskJointPosVelAccBounds::getPositionLowerBounds() const { |
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return m_qMin; |
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} |
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const Vector& TaskJointPosVelAccBounds::getPositionUpperBounds() const { |
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return m_qMax; |
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} |
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void TaskJointPosVelAccBounds::setTimeStep(double dt) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT(dt > 0.0, "dt needs to be positive"); |
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m_dt = dt; |
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} |
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void TaskJointPosVelAccBounds::setVerbose(bool verbose) { m_verbose = verbose; } |
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void TaskJointPosVelAccBounds::setPositionBounds(ConstRefVector lower, |
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ConstRefVector upper) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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lower.size() == m_na, |
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"The size of the lower position bounds vector needs to equal " + |
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std::to_string(m_na)); |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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upper.size() == m_na, |
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"The size of the upper position bounds vector needs to equal " + |
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std::to_string(m_na)); |
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m_qMin = lower; |
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m_qMax = upper; |
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m_impose_position_bounds = true; |
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m_impose_viability_bounds = true; |
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} |
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void TaskJointPosVelAccBounds::setVelocityBounds(ConstRefVector upper) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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upper.size() == m_na, |
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"The size of the (absolute) velocity bounds vector needs to equal " + |
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std::to_string(m_na)); |
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m_dqMax = upper; |
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m_impose_velocity_bounds = true; |
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} |
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void TaskJointPosVelAccBounds::setAccelerationBounds(ConstRefVector upper) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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upper.size() == m_na, |
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"The size of the (absolute) acceleration bounds vector needs to equal " + |
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std::to_string(m_na)); |
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m_ddqMax = upper; |
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m_impose_acceleration_bounds = true; |
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} |
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const ConstraintBase& TaskJointPosVelAccBounds::getConstraint() const { |
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return m_constraint; |
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} |
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const ConstraintBase& TaskJointPosVelAccBounds::compute(const double, |
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ConstRefVector q, |
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ConstRefVector v, |
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Data&) { |
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// getProfiler().start("TaskJointPosVelAccBounds"); |
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// Eigen::internal::set_is_malloc_allowed(false); |
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computeAccLimits(q, v, m_verbose); |
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m_constraint.upperBound() = m_ddqUB; |
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m_constraint.lowerBound() = m_ddqLB; |
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// Eigen::internal::set_is_malloc_allowed(true); |
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// getProfiler().stop("TaskJointPosVelAccBounds"); |
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// getProfiler().report_all(9, std::cout); |
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return m_constraint; |
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} |
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void TaskJointPosVelAccBounds::setImposeBounds( |
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bool impose_position_bounds, bool impose_velocity_bounds, |
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bool impose_viability_bounds, bool impose_acceleration_bounds) { |
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m_impose_position_bounds = impose_position_bounds; |
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m_impose_velocity_bounds = impose_velocity_bounds; |
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m_impose_viability_bounds = impose_viability_bounds; |
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m_impose_acceleration_bounds = impose_acceleration_bounds; |
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} |
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void TaskJointPosVelAccBounds::isStateViable(ConstRefVector qa, |
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ConstRefVector dqa, bool verbose) { |
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m_viabViol.setZero(m_na); |
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for (int i = 0; i < m_na; i++) { |
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if (qa[i] < (m_qMin[i] - m_eps)) { |
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if (verbose) { |
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std::cout << "State of joint " << i |
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<< " is not viable because q[i]< qMin[i] : " << qa[i] << "<" |
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<< m_qMin[i] << std::endl; |
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} |
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m_viabViol[i] = m_qMin[i] - qa[i]; |
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} |
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if (qa[i] > (m_qMax[i] + m_eps)) { |
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if (verbose) { |
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std::cout << "State of joint " << i |
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<< " is not viable because qa[i]>m_qMax[i] : " << qa[i] << ">" |
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<< m_qMax[i] << std::endl; |
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} |
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m_viabViol[i] = qa[i] - m_qMax[i]; |
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} |
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if (std::abs(dqa[i]) > (m_dqMax[i] + m_eps)) { |
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if (verbose) { |
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std::cout << "State (q,dq) :(" << qa[i] << "," << dqa[i] |
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<< ") of joint " << i |
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<< " is not viable because |dq|>dqMax : " << std::abs(dqa[i]) |
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<< ">" << m_dqMax[i] << std::endl; |
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} |
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m_viabViol[i] = std::abs(dqa[i]) - m_dqMax[i]; |
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} |
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double dqMaxViab = |
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std::sqrt(std::max(0.0, 2 * m_ddqMax[i] * (m_qMax[i] - qa[i]))); |
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if (dqa[i] > (dqMaxViab + m_eps)) { |
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if (verbose) { |
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std::cout << "State (q,dq,dqMaxViab) :(" << qa[i] << "," << dqa[i] |
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<< "," << dqMaxViab << ") of joint " << i |
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<< " is not viable because dq>dqMaxViab : " << dqa[i] << ">" |
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<< dqMaxViab << std::endl; |
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} |
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m_viabViol[i] = dqa[i] - dqMaxViab; |
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} |
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double dqMinViab = |
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-std::sqrt(std::max(0.0, 2 * m_ddqMax[i] * (qa[i] - m_qMin[i]))); |
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if (dqa[i] < (dqMinViab + m_eps)) { |
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if (verbose) { |
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std::cout << "State (q,dq,dqMinViab) :(" << qa[i] << "," << dqa[i] |
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<< "," << dqMinViab << ") of joint " << i |
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<< " is not viable because dq<dqMinViab : " << dqa[i] << "<" |
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<< dqMinViab << std::endl; |
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} |
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m_viabViol[i] = dqMinViab - dqa[i]; |
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} |
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} |
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} |
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✗ |
void TaskJointPosVelAccBounds::computeAccLimitsFromPosLimits(ConstRefVector qa, |
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ConstRefVector dqa, |
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bool verbose) { |
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✗ |
m_ddqMax_q3 = m_two_dt_sq * (m_qMax - qa - m_dt * dqa); |
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m_ddqMin_q3 = m_two_dt_sq * (m_qMin - qa - m_dt * dqa); |
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m_ddqMax_q2.setZero(m_na); |
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m_ddqMin_q2.setZero(m_na); |
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m_ddqLBPos.setConstant(m_na, 1, -1e10); |
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m_ddqUBPos.setConstant(m_na, 1, 1e10); |
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m_minus_dq_over_dt = -dqa / m_dt; |
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for (int i = 0; i < m_na; i++) { |
290 |
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if (dqa[i] <= 0.0) { |
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m_ddqUBPos[i] = m_ddqMax_q3[i]; |
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if (m_ddqMin_q3[i] < m_minus_dq_over_dt[i]) { |
293 |
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m_ddqLBPos[i] = m_ddqMin_q3[i]; |
294 |
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} else if (qa[i] != m_qMin[i]) { |
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m_ddqMin_q2[i] = (dqa[i] * dqa[i]) / (2.0 * (qa[i] - m_qMin[i])); |
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m_ddqLBPos[i] = std::max(m_ddqMin_q2[i], m_minus_dq_over_dt[i]); |
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} else { |
298 |
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if (verbose == true) { |
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std::cout << "WARNING qa[i]==m_qMin[i] for joint" << i << std::endl; |
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std::cout << "You are going to violate the position bound " << i |
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<< std::endl; |
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} |
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m_ddqLBPos[i] = 0.0; |
304 |
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} |
305 |
|
|
} else { |
306 |
|
✗ |
m_ddqLBPos[i] = m_ddqMin_q3[i]; |
307 |
|
✗ |
if (m_ddqMax_q3[i] > m_minus_dq_over_dt[i]) { |
308 |
|
✗ |
m_ddqUBPos[i] = m_ddqMax_q3[i]; |
309 |
|
✗ |
} else if (qa[i] != m_qMax[i]) { |
310 |
|
✗ |
m_ddqMax_q2[i] = -(dqa[i] * dqa[i]) / (2 * (m_qMax[i] - qa[i])); |
311 |
|
✗ |
m_ddqUBPos[i] = std::min(m_ddqMax_q2[i], m_minus_dq_over_dt[i]); |
312 |
|
|
} else { |
313 |
|
✗ |
if (verbose == true) { |
314 |
|
✗ |
std::cout << "WARNING qa[i]==m_qMax[i] for joint" << i << std::endl; |
315 |
|
✗ |
std::cout << "You are going to violate the position bound " << i |
316 |
|
✗ |
<< std::endl; |
317 |
|
|
} |
318 |
|
✗ |
m_ddqUBPos[i] = 0.0; |
319 |
|
|
} |
320 |
|
|
} |
321 |
|
|
} |
322 |
|
|
} |
323 |
|
✗ |
void TaskJointPosVelAccBounds::computeAccLimitsFromViability(ConstRefVector qa, |
324 |
|
|
ConstRefVector dqa, |
325 |
|
|
bool verbose) { |
326 |
|
✗ |
m_ddqLBVia.setConstant(m_na, 1, -1e10); |
327 |
|
✗ |
m_ddqUBVia.setConstant(m_na, 1, 1e10); |
328 |
|
✗ |
m_dt_dq = m_dt * dqa; |
329 |
|
✗ |
m_minus_dq_over_dt = -dqa / m_dt; |
330 |
|
✗ |
m_dt_two_dq = 2 * m_dt_dq; |
331 |
|
✗ |
m_two_ddqMax = 2 * m_ddqMax; |
332 |
|
✗ |
m_dt_ddqMax_dt = m_ddqMax * m_dt_square; |
333 |
|
✗ |
m_dq_square = dqa.cwiseProduct(dqa); |
334 |
|
✗ |
m_q_plus_dt_dq = qa + m_dt_dq; |
335 |
|
✗ |
m_b_1 = m_dt_two_dq + m_dt_ddqMax_dt; |
336 |
|
✗ |
m_b_2 = m_dt_two_dq - m_dt_ddqMax_dt; |
337 |
|
✗ |
m_ddq_1.setZero(m_na); |
338 |
|
✗ |
m_ddq_2.setZero(m_na); |
339 |
|
✗ |
m_c_1 = m_dq_square - m_two_ddqMax.cwiseProduct(m_qMax - m_q_plus_dt_dq); |
340 |
|
✗ |
m_delta_1 = m_b_1.cwiseProduct(m_b_1) - 2 * m_two_a * m_c_1; |
341 |
|
✗ |
m_c_2 = m_dq_square - m_two_ddqMax.cwiseProduct(m_q_plus_dt_dq - m_qMin); |
342 |
|
✗ |
m_delta_2 = m_b_2.cwiseProduct(m_b_2) - 2 * m_two_a * m_c_2; |
343 |
|
✗ |
for (int i = 0; i < m_na; i++) { |
344 |
|
✗ |
if (m_delta_1[i] >= 0.0) { |
345 |
|
✗ |
m_ddq_1[i] = (-m_b_1[i] + std::sqrt(m_delta_1[i])) / (m_two_a); |
346 |
|
|
} else { |
347 |
|
✗ |
m_ddq_1[i] = m_minus_dq_over_dt[i]; |
348 |
|
✗ |
if (verbose == true) { |
349 |
|
✗ |
std::cout << "Error: state (" << qa[i] << "," << dqa[i] << ") of joint " |
350 |
|
✗ |
<< i << "not viable because delta is negative: " << m_delta_1 |
351 |
|
✗ |
<< std::endl; |
352 |
|
|
} |
353 |
|
|
} |
354 |
|
✗ |
if (m_delta_2[i] >= 0.0) { |
355 |
|
✗ |
m_ddq_2[i] = (-m_b_2[i] - std::sqrt(m_delta_2[i])) / (m_two_a); |
356 |
|
|
} else { |
357 |
|
✗ |
m_ddq_2[i] = m_minus_dq_over_dt[i]; |
358 |
|
✗ |
if (verbose == true) { |
359 |
|
✗ |
std::cout << "Error: state (" << qa[i] << "," << dqa[i] << ") of joint " |
360 |
|
✗ |
<< i << "not viable because delta is negative: " << m_delta_2 |
361 |
|
✗ |
<< std::endl; |
362 |
|
|
} |
363 |
|
|
} |
364 |
|
|
} |
365 |
|
✗ |
m_ddqUBVia = m_ddq_1.cwiseMax(m_minus_dq_over_dt); |
366 |
|
✗ |
m_ddqLBVia = m_ddq_2.cwiseMin(m_minus_dq_over_dt); |
367 |
|
|
} |
368 |
|
|
|
369 |
|
✗ |
void TaskJointPosVelAccBounds::computeAccLimits(ConstRefVector q, |
370 |
|
|
ConstRefVector dq, |
371 |
|
|
bool verbose) { |
372 |
|
✗ |
m_qa = q.tail(m_na); |
373 |
|
✗ |
m_dqa = dq.tail(m_na); |
374 |
|
✗ |
isStateViable(m_qa, m_dqa, m_verbose); |
375 |
|
✗ |
if (verbose == true) { |
376 |
|
✗ |
for (int i = 0; i < m_na; i++) { |
377 |
|
✗ |
if (m_viabViol[i] > m_eps) { |
378 |
|
✗ |
std::cout << "WARNING: specified state ( < " << m_qa[i] << " , " |
379 |
|
✗ |
<< m_dqa[i] << ") is not viable violation : " << m_viabViol[i] |
380 |
|
✗ |
<< std::endl; |
381 |
|
|
} |
382 |
|
|
} |
383 |
|
|
} |
384 |
|
|
|
385 |
|
|
// Acceleration limits imposed by position bounds |
386 |
|
✗ |
if (m_impose_position_bounds == true) { |
387 |
|
✗ |
computeAccLimitsFromPosLimits(m_qa, m_dqa, verbose); |
388 |
|
|
} |
389 |
|
|
// Acceleration limits imposed by velocity bounds |
390 |
|
|
// dq[t+1] = dq + dt*ddq < dqMax |
391 |
|
|
// ddqMax = (dqMax-dq)/dt |
392 |
|
|
// ddqMin = (dqMin-dq)/dt = (-dqMax-dq)/dt |
393 |
|
✗ |
m_ddqLBVel.setConstant(m_na, 1, -1e10); |
394 |
|
✗ |
m_ddqUBVel.setConstant(m_na, 1, 1e10); |
395 |
|
✗ |
if (m_impose_velocity_bounds == true) { |
396 |
|
✗ |
m_ddqLBVel = (-m_dqMax - m_dqa) / m_dt; |
397 |
|
✗ |
m_ddqUBVel = (m_dqMax - m_dqa) / m_dt; |
398 |
|
|
} |
399 |
|
|
// Acceleration limits imposed by viability |
400 |
|
✗ |
if (m_impose_viability_bounds == true) { |
401 |
|
✗ |
computeAccLimitsFromViability(m_qa, m_dqa, verbose); |
402 |
|
|
} |
403 |
|
|
// Acceleration limits |
404 |
|
✗ |
m_ddqLBAcc.setConstant(m_na, 1, -1e10); |
405 |
|
✗ |
m_ddqUBAcc.setConstant(m_na, 1, 1e10); |
406 |
|
✗ |
if (m_impose_acceleration_bounds == true) { |
407 |
|
✗ |
m_ddqLBAcc = -m_ddqMax; |
408 |
|
✗ |
m_ddqUBAcc = m_ddqMax; |
409 |
|
|
} |
410 |
|
|
// Take the most conservative limit for each joint |
411 |
|
✗ |
m_ub.setConstant(4, 1, 1e10); |
412 |
|
✗ |
m_lb.setConstant(4, 1, -1e10); |
413 |
|
✗ |
m_ddqLB.setConstant(m_na, 1, -1e10); |
414 |
|
✗ |
m_ddqUB.setConstant(m_na, 1, 1e10); |
415 |
|
✗ |
for (int i = 0; i < m_na; i++) { |
416 |
|
✗ |
m_ub[0] = m_ddqUBPos[i]; |
417 |
|
✗ |
m_ub[1] = m_ddqUBVia[i]; |
418 |
|
✗ |
m_ub[2] = m_ddqUBVel[i]; |
419 |
|
✗ |
m_ub[3] = m_ddqUBAcc[i]; |
420 |
|
|
|
421 |
|
✗ |
m_lb[0] = m_ddqLBPos[i]; |
422 |
|
✗ |
m_lb[1] = m_ddqLBVia[i]; |
423 |
|
✗ |
m_lb[2] = m_ddqLBVel[i]; |
424 |
|
✗ |
m_lb[3] = m_ddqLBAcc[i]; |
425 |
|
|
|
426 |
|
✗ |
m_ddqLB[i] = m_lb.maxCoeff(); |
427 |
|
✗ |
m_ddqUB[i] = m_ub.minCoeff(); |
428 |
|
|
|
429 |
|
✗ |
if (m_ddqUB[i] < m_ddqLB[i]) { |
430 |
|
✗ |
if (verbose == true) { |
431 |
|
✗ |
std::cout << "Conflict between pos/vel/acc bound ddqMin " << m_ddqLB[i] |
432 |
|
✗ |
<< " ddqMax " << m_ddqUB[i] << std::endl; |
433 |
|
✗ |
std::cout << "ub " << m_ub.transpose() << std::endl; |
434 |
|
✗ |
std::cout << "lb " << m_lb.transpose() << std::endl; |
435 |
|
|
} |
436 |
|
✗ |
if (m_ddqUB[i] == m_ub[0]) { |
437 |
|
✗ |
m_ddqLB[i] = m_ddqUB[i]; |
438 |
|
|
} else { |
439 |
|
✗ |
m_ddqUB[i] = m_ddqLB[i]; |
440 |
|
|
} |
441 |
|
✗ |
if (verbose == true) { |
442 |
|
✗ |
std::cout << "New bounds are ddqMin " << m_ddqLB[i] << " ddqMax " |
443 |
|
✗ |
<< m_ddqUB[i] << std::endl; |
444 |
|
|
} |
445 |
|
|
} |
446 |
|
|
} |
447 |
|
|
} |
448 |
|
|
} // namespace tasks |
449 |
|
|
} // namespace tsid |
450 |
|
|
|