92 lines
3.0 KiB
C++
92 lines
3.0 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file InverseKinematicsExampleExpressions.cpp
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* @brief Implement inverse kinematics on a three-link arm using expressions.
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* @date April 15, 2019
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* @author Frank Dellaert
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*/
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#include <gtsam/geometry/Pose2.h>
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#include <gtsam/nonlinear/ExpressionFactorGraph.h>
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#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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#include <gtsam/nonlinear/Marginals.h>
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#include <gtsam/nonlinear/expressions.h>
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#include <gtsam/slam/BetweenFactor.h>
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#include <gtsam/slam/expressions.h>
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#include <cmath>
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using namespace std;
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using namespace gtsam;
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// Scalar multiplication of a vector, with derivatives.
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inline Vector3 scalarMultiply(const double& s, const Vector3& v,
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OptionalJacobian<3, 1> Hs,
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OptionalJacobian<3, 3> Hv) {
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if (Hs) *Hs = v;
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if (Hv) *Hv = s * I_3x3;
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return s * v;
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}
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// Expression version of scalar product, using above function.
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inline Vector3_ operator*(const Double_& s, const Vector3_& v) {
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return Vector3_(&scalarMultiply, s, v);
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}
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// Expression version of Pose2::Expmap
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inline Pose2_ Expmap(const Vector3_& xi) { return Pose2_(&Pose2::Expmap, xi); }
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// Main function
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int main(int argc, char** argv) {
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// Three-link planar manipulator specification.
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const double L1 = 3.5, L2 = 3.5, L3 = 2.5; // link lengths
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const Pose2 sXt0(0, L1 + L2 + L3, M_PI / 2); // end-effector pose at rest
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const Vector3 xi1(0, 0, 1), xi2(L1, 0, 1),
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xi3(L1 + L2, 0, 1); // screw axes at rest
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// Create Expressions for unknowns
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using symbol_shorthand::Q;
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Double_ q1(Q(1)), q2(Q(2)), q3(Q(3));
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// Forward kinematics expression as product of exponentials
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Pose2_ l1Zl1 = Expmap(q1 * Vector3_(xi1));
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Pose2_ l2Zl2 = Expmap(q2 * Vector3_(xi2));
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Pose2_ l3Zl3 = Expmap(q3 * Vector3_(xi3));
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Pose2_ forward = compose(compose(l1Zl1, l2Zl2), compose(l3Zl3, Pose2_(sXt0)));
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// Create a factor graph with a a single expression factor.
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ExpressionFactorGraph graph;
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Pose2 desiredEndEffectorPose(3, 2, 0);
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auto model = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
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graph.addExpressionFactor(forward, desiredEndEffectorPose, model);
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// Create initial estimate
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Values initial;
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initial.insert(Q(1), 0.1);
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initial.insert(Q(2), 0.2);
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initial.insert(Q(3), 0.3);
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initial.print("\nInitial Estimate:\n"); // print
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GTSAM_PRINT(forward.value(initial));
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// Optimize the initial values using a Levenberg-Marquardt nonlinear optimizer
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LevenbergMarquardtParams params;
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params.setlambdaInitial(1e6);
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LevenbergMarquardtOptimizer optimizer(graph, initial, params);
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Values result = optimizer.optimize();
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result.print("Final Result:\n");
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GTSAM_PRINT(forward.value(result));
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return 0;
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}
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