This repository contains a C++ static library for implementing the forward and inverse kinematics of a three-tube concentric tube robot (CTR) based on the Cosserat Theory-based kinematic model as described in the paper:
[1] D. C. Rucker, B. A. Jones, and R. J. Webster III, “A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots,” IEEE Trans. Robot., vol. 26, no. 5, pp. 769–780, Oct. 2010, doi: 10.1109/TRO.2010.2062570.
This C++ static library provides a barebone implementation of the forward and inverse kinematics of a three-tube concentric tube robot based on the Cosserat Theory-based kinematic model. As part of my PhD at Western University in London, Ontario, Canada, I have developed this C++ static library to provide a reliable and efficient implementation of the forward and inverse kinematics for a three-tube CTR. The library is based on the Cosserat Theory-based kinematic model as described in [1]. Concentric tube robots have applications in medical robotics and minimally invasive procedures.
- Implementation of the forward kinematics of a three-tube CTR.
- Implementation of the inverse kinematics of a three-tube CTR.
- Easy-to-use API for integrating the library into your C++ projects.
- Comprehensive documentation explaining the kinematic model and usage of the library.
To use this library, you can either clone the repository and build it from source as a CMAKE project (recommended) or download the precompiled binaries for your platform from the Releases section.
Before using the library, ensure that you have the following libraries installed in your system:
- Clone the repository:
git clone https://github.com/fcpedrosa/Concentric-Tube-Robot- Build the library:
cd repo-name
mkdir build && cd build
cmake ..
make -j4- The library will be built as a static library (
CTR.a).
Download the precompiled binaries for your platform from the Releases section (TBA). Add the library to your C++ project's dependencies and include the appropriate header files.
To use the library in your C++ project, you need to include the necessary header files and link against the library. Here's a simple example:
#include <iostream>
// include the CTR library header
#include "CTR.hpp"
int main()
{
// # # # # # # # # ---- Properties of Nitinol Tubes ---- # # # # # # # #
double E = 58.00E9; // Young's modulus GPa
double G = 25.50E9; // Shear modulus GPa
// Precurvature radii for the tubes
double R1 = 40.00E-3; // (4cm curvature radius)
double R2 = 10.00E-3; // (10 cm curvature radius)
double R3 = 14.00E-3; // (14 cm curvature radius)
// -- ** -- Precurvature vectors (for curved portions of the tubes) -- ** -- [u_x* u_y* 0]
blaze::StaticVector<double, 3UL> u1 = {1.00 / R1, 0.00, 0.00};
blaze::StaticVector<double, 3UL> u2 = {1.00 / R2, 0.00, 0.00};
blaze::StaticVector<double, 3UL> u3 = {1.00 / R3, 0.00, 0.00};
// defining the kinematic parameters of the robot
// --** --Lengths of the tubes' straight sections (meters) -- ** --
blaze::StaticVector<double, 3UL> ls = {190.00E-3, 120.00E-3, 90.00E-3}; // 190, 120, 100
// --** --Lengths of the tubes' curved sections (meters) -- ** --
blaze::StaticVector<double, 3UL> lc = {60.00E-3, 80.00E-3, 40.00E-3}; // 60, 80, 50;
// --** --Outer and Inner diameters of the tubes (meters)--** --
blaze::StaticVector<double, 3UL> OD = {0.92e-3, 1.10E-3, 1.40E-3};
blaze::StaticVector<double, 3UL> ID = {0.80E-3, 0.97e-3, 1.20E-3};
// # # # # # ---- Instantiating the three Tube objects ---- # # # # #
std::shared_ptr<Tube> T1 = std::make_shared<Tube>(OD[0UL], ID[0UL], E, G, ls[0UL], lc[0UL], u1); // innermost tube
std::shared_ptr<Tube> T2 = std::make_shared<Tube>(OD[1UL], ID[1UL], E, G, ls[1UL], lc[1UL], u2); // intermediate tube
std::shared_ptr<Tube> T3 = std::make_shared<Tube>(OD[2UL], ID[2UL], E, G, ls[2UL], lc[2UL], u3); // outermost tube
// instantiating an array of smart pointers to CTR component tubes
std::array<std::shared_ptr<Tube>, 3UL> Tb = {T1, T2, T3};
// initial joint actuation values "home position" - q = [Beta Alpha]
blaze::StaticVector<double, 3UL> Beta_0 = {-120.00E-3, -100.00E-3, -80.00E-3}; // 130, 100, 50 | 130, 100,
blaze::StaticVector<double, 3UL> Alpha_0 = {mathOp::deg2Rad(0.00), mathOp::deg2Rad(0.00), mathOp::deg2Rad(0.00)};
blaze::StaticVector<double, 6UL> q_0;
blaze::subvector<0UL, 3UL>(q_0) = Beta_0;
blaze::subvector<3UL, 3UL>(q_0) = Alpha_0;
// Determining the accuracy of BVP solutions
double Tol = 1.00E-6;
// tolerance for position control (0.5 mm)
double pos_tol = 5.00E-4;
// # # # # # ---- Instantiating the CTR object ---- # # # # #
CTR CTR_robot(Tb, q_0, Tol, mathOp::rootFindingMethod::MODIFIED_NEWTON_RAPHSON);
// initial guess for the BVP
blaze::StaticVector<double, 5UL> initGuess;
// You can set external wrenches acting as point loads on the distal ends of the robot as
blaze::StaticVector<double, 3UL> moment = {0.00, -0.05, 0.00}, force = {0.00, -0.15, -0.55};
// setting the external point moment
CTR_robot.setDistalMoment(moment);
// setting the external point force
CTR_robot.setDistalForce(force);
// Actuates the robot to the configuration q_0 and solves the corresponding FK problem
CTR_robot.actuate_CTR(initGuess, q_0);
// inspect the distal end's position after actuation
std::cout << "Tip position: " << blaze::trans(CTR_robot.getTipPos()) << std::endl;
// Testing the differential kinematics-based position control for the CTR
blaze::StaticVector<double, 3UL> tip_pos, target = { -0.053210, 0.043606, 0.179527 };
// inverse kinematics
CTR_robot.posCTRL(initGuess, target, pos_tol);
tip_pos = CTR_robot.getTipPos();
std::cout << "Target is: " << blaze::trans(target)
<< "Tip position is: " << blaze::trans(tip_pos)
<< "Joint values (IK solution): " << blaze::trans(CTR_robot.getConfiguration())
<< "Position error: " << blaze::norm(tip_pos - target) * 1.00E3 << " [mm]"
<< std::endl;
return 0;
}For detailed documentation on the library's API and usage, refer to the Documentation section.
The examples directory contains some usage examples to help you get started.
Contributions to this project are welcome! If you find any issues or have ideas for improvements, please open an issue or submit a pull request.
This project is licensed under the MIT License - see the LICENSE file for details.
For any questions or inquiries, feel free to contact me:
Filipe Pedrosa Email: fpedrosa@uwo.ca
Please note that this project is a research-oriented implementation and comes with no warranty or support. Use it at your own risk.