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