joint_impedance_control.cpp

An example showing a joint impedance type control that executes a Cartesian motion in the shape of a circle.

An example showing a joint impedance type control that executes a Cartesian motion in the shape of a circle. The example illustrates how to use the internal inverse kinematics to map a Cartesian trajectory to joint space. The joint space target is tracked by an impedance control that additionally compensates coriolis terms using the libfranka model library. This example also serves to compare commanded vs. measured torques. The results are printed from a separate thread to avoid blocking print functions in the real-time loop.

// Copyright (c) 2023 Franka Robotics GmbH
// Use of this source code is governed by the Apache-2.0 license, see LICENSE
#include <array>
#include <atomic>
#include <cmath>
#include <functional>
#include <iostream>
#include <iterator>
#include <mutex>
#include <thread>
 
#include <franka/duration.h>
#include <franka/exception.h>
#include <franka/model.h>
#include <franka/rate_limiting.h>
#include <franka/robot.h>
 
#include "examples_common.h"
 
namespace {
template <class T, size_t N>
std::ostream& operator<<(std::ostream& ostream, const std::array<T, N>& array) {
  ostream << "[";
  std::copy(array.cbegin(), array.cend() - 1, std::ostream_iterator<T>(ostream, ","));
  std::copy(array.cend() - 1, array.cend(), std::ostream_iterator<T>(ostream));
  ostream << "]";
  return ostream;
}
}  // anonymous namespace
 
int main(int argc, char** argv) {
  // Check whether the required arguments were passed.
  if (argc != 2) {
    std::cerr << "Usage: " << argv[0] << " <robot-hostname>" << std::endl;
    return -1;
  }
  // Set and initialize trajectory parameters.
  const double radius = 0.05;
  const double vel_max = 0.25;
  const double acceleration_time = 2.0;
  const double run_time = 20.0;
  // Set print rate for comparing commanded vs. measured torques.
  const double print_rate = 10.0;
 
  double vel_current = 0.0;
  double angle = 0.0;
  double time = 0.0;
 
  // Initialize data fields for the print thread.
  struct {
    std::mutex mutex;
    bool has_data;
    std::array<double, 7> tau_d_last;
    franka::RobotState robot_state;
    std::array<double, 7> gravity;
  } print_data{};
  std::atomic_bool running{true};
 
  // Start print thread.
  std::thread print_thread([print_rate, &print_data, &running]() {
    while (running) {
      // Sleep to achieve the desired print rate.
      std::this_thread::sleep_for(
          std::chrono::milliseconds(static_cast<int>((1.0 / print_rate * 1000.0))));
 
      // Try to lock data to avoid read write collisions.
      if (print_data.mutex.try_lock()) {
        if (print_data.has_data) {
          std::array<double, 7> tau_error{};
          double error_rms(0.0);
          std::array<double, 7> tau_d_actual{};
          for (size_t i = 0; i < 7; ++i) {
            tau_d_actual[i] = print_data.tau_d_last[i] + print_data.gravity[i];
            tau_error[i] = tau_d_actual[i] - print_data.robot_state.tau_J[i];
            error_rms += std::pow(tau_error[i], 2.0) / tau_error.size();
          }
          error_rms = std::sqrt(error_rms);
 
          // Print data to console
          std::cout << "tau_error [Nm]: " << tau_error << std::endl
                    << "tau_commanded [Nm]: " << tau_d_actual << std::endl
                    << "tau_measured [Nm]: " << print_data.robot_state.tau_J << std::endl
                    << "root mean square of tau_error [Nm]: " << error_rms << std::endl
                    << "-----------------------" << std::endl;
          print_data.has_data = false;
        }
        print_data.mutex.unlock();
      }
    }
  });
 
  try {
    // Connect to robot.
    franka::Robot robot(argv[1]);
    setDefaultBehavior(robot);
 
    // First move the robot to a suitable joint configuration
    std::array<double, 7> q_goal = {{0, -M_PI_4, 0, -3 * M_PI_4, 0, M_PI_2, M_PI_4}};
    MotionGenerator motion_generator(0.5, q_goal);
    std::cout << "WARNING: This example will move the robot! "
              << "Please make sure to have the user stop button at hand!" << std::endl
              << "Press Enter to continue..." << std::endl;
    std::cin.ignore();
    robot.control(motion_generator);
    std::cout << "Finished moving to initial joint configuration." << std::endl;
 
    // Set additional parameters always before the control loop, NEVER in the control loop!
    // Set collision behavior.
    robot.setCollisionBehavior(
        {{20.0, 20.0, 18.0, 18.0, 16.0, 14.0, 12.0}}, {{20.0, 20.0, 18.0, 18.0, 16.0, 14.0, 12.0}},
        {{20.0, 20.0, 18.0, 18.0, 16.0, 14.0, 12.0}}, {{20.0, 20.0, 18.0, 18.0, 16.0, 14.0, 12.0}},
        {{20.0, 20.0, 20.0, 25.0, 25.0, 25.0}}, {{20.0, 20.0, 20.0, 25.0, 25.0, 25.0}},
        {{20.0, 20.0, 20.0, 25.0, 25.0, 25.0}}, {{20.0, 20.0, 20.0, 25.0, 25.0, 25.0}});
 
    // Load the kinematics and dynamics model.
    franka::Model model = robot.loadModel();
 
    std::array<double, 16> initial_pose;
 
    // Define callback function to send Cartesian pose goals to get inverse kinematics solved.
    auto cartesian_pose_callback = [=, &time, &vel_current, &running, &angle, &initial_pose](
                                       const franka::RobotState& robot_state,
                                       franka::Duration period) -> franka::CartesianPose {
      // Update time.
      time += period.toSec();
 
      if (time == 0.0) {
        // Read the initial pose to start the motion from in the first time step.
        initial_pose = robot_state.O_T_EE_c;
      }
 
      // Compute Cartesian velocity.
      if (vel_current < vel_max && time < run_time) {
        vel_current += period.toSec() * std::fabs(vel_max / acceleration_time);
      }
      if (vel_current > 0.0 && time > run_time) {
        vel_current -= period.toSec() * std::fabs(vel_max / acceleration_time);
      }
      vel_current = std::fmax(vel_current, 0.0);
      vel_current = std::fmin(vel_current, vel_max);
 
      // Compute new angle for our circular trajectory.
      angle += period.toSec() * vel_current / std::fabs(radius);
      if (angle > 2 * M_PI) {
        angle -= 2 * M_PI;
      }
 
      // Compute relative y and z positions of desired pose.
      double delta_y = radius * (1 - std::cos(angle));
      double delta_z = radius * std::sin(angle);
      franka::CartesianPose pose_desired = initial_pose;
      pose_desired.O_T_EE[13] += delta_y;
      pose_desired.O_T_EE[14] += delta_z;
 
      // Send desired pose.
      if (time >= run_time + acceleration_time) {
        running = false;
        return franka::MotionFinished(pose_desired);
      }
 
      return pose_desired;
    };
 
    // Set gains for the joint impedance control.
    // Stiffness
    const std::array<double, 7> k_gains = {{600.0, 600.0, 600.0, 600.0, 250.0, 150.0, 50.0}};
    // Damping
    const std::array<double, 7> d_gains = {{50.0, 50.0, 50.0, 50.0, 30.0, 25.0, 15.0}};
 
    // Define callback for the joint torque control loop.
    std::function<franka::Torques(const franka::RobotState&, franka::Duration)>
        impedance_control_callback =
            [&print_data, &model, k_gains, d_gains](
                const franka::RobotState& state, franka::Duration /*period*/) -> franka::Torques {
      // Read current coriolis terms from model.
      std::array<double, 7> coriolis = model.coriolis(state);
 
      // Compute torque command from joint impedance control law.
      // Note: The answer to our Cartesian pose inverse kinematics is always in state.q_d with one
      // time step delay.
      std::array<double, 7> tau_d_calculated;
      for (size_t i = 0; i < 7; i++) {
        tau_d_calculated[i] =
            k_gains[i] * (state.q_d[i] - state.q[i]) - d_gains[i] * state.dq[i] + coriolis[i];
      }
 
      // The following line is only necessary for printing the rate limited torque. As we activated
      // rate limiting for the control loop (activated by default), the torque would anyway be
      // adjusted!
      std::array<double, 7> tau_d_rate_limited =
          franka::limitRate(franka::kMaxTorqueRate, tau_d_calculated, state.tau_J_d);
 
      // Update data to print.
      if (print_data.mutex.try_lock()) {
        print_data.has_data = true;
        print_data.robot_state = state;
        print_data.tau_d_last = tau_d_rate_limited;
        print_data.gravity = model.gravity(state);
        print_data.mutex.unlock();
      }
 
      // Send torque command.
      return tau_d_rate_limited;
    };
 
    // Start real-time control loop.
    robot.control(impedance_control_callback, cartesian_pose_callback);
 
  } catch (const franka::Exception& ex) {
    running = false;
    std::cerr << ex.what() << std::endl;
  }
 
  if (print_thread.joinable()) {
    print_thread.join();
  }
  return 0;
}