Example 14: Tracking of arbitrary signals with Velocity, Acceleration, and Jerk Limits

C++

// Only with Ruckig Pro
 
#include <cmath>
#include <iostream>
 
#include <ruckig/trackig.hpp>
 
 
using namespace ruckig;
 
// Create the target state signal
TargetState<1> model_ramp(double t, double ramp_vel=0.5, double ramp_pos=1.0) {
    TargetState<1> target;
    const bool on_ramp = t < ramp_pos / std::abs(ramp_vel);
    target.position[0] = on_ramp ? t * ramp_vel : ramp_pos;
    target.velocity[0] = on_ramp ? ramp_vel : 0.0;
    target.acceleration[0] = 0.0;
    return target;
}
 
TargetState<1> model_constant_acceleration(double t, double ramp_acc=0.05) {
    TargetState<1> target;
    target.position[0] = t * t * ramp_acc;
    target.velocity[0] = t * ramp_acc;
    target.acceleration[0] = ramp_acc;
    return target;
}
 
TargetState<1> model_sinus(double t, double ramp_vel=0.4) {
    TargetState<1> target;
    target.position[0] = std::sin(ramp_vel * t);
    target.velocity[0] = ramp_vel * std::cos(ramp_vel * t);
    target.acceleration[0] = -ramp_vel * ramp_vel * std::sin(ramp_vel * t);
    return target;
}
 
 
int main() {
    // Create instances: the Trackig OTG as well as input and output parameters
    Trackig<1> otg {0.01};  // control cycle
    InputParameter<1> input;
    OutputParameter<1> output;
 
    // Set input parameters
    input.current_position = {0.0};
    input.current_velocity = {0.0};
    input.current_acceleration = {0.0};
 
    input.max_velocity = {0.8};
    input.max_acceleration = {2.0};
    input.max_jerk = {5.0};
 
    // Optional minimum and maximum position
    input.min_position = {-2.5};
    input.max_position = {2.5};
 
    otg.reactiveness = 1.0; // default value, should be in [0, 1]
 
    // Generate the trajectory within the control loop
    std::cout << "target | follow" << std::endl;
    for (size_t t = 0; t < 500; t += 1) {
        auto target_state = model_ramp(otg.delta_time * t);
        auto res = otg.update(target_state, input, output);
        std::cout << target_state.position[0] << " " << output.new_position[0] << std::endl;
 
        output.pass_to_input(input);
    }
}

Python

# Only with Ruckig Pro
 
from math import sin, cos
from pathlib import Path
from sys import path
 
# Path to the build directory including a file similar to 'ruckig.cpython-37m-x86_64-linux-gnu'.
build_path = Path(__file__).parent.absolute().parent / 'build'
path.insert(0, str(build_path))
 
from ruckig import Trackig, TargetState, InputParameter, OutputParameter
 
 
# Create the target state signal
def model_ramp(t, ramp_vel=0.5, ramp_pos=1.0):
    target = TargetState(1)
    on_ramp = t < ramp_pos / abs(ramp_vel)
    target.position = [t * ramp_vel] if on_ramp else [ramp_pos]
    target.velocity = [ramp_vel] if on_ramp else [0.0]
    target.acceleration = [0.0]
    return target
 
def model_constant_acceleration(t, ramp_acc=0.05):
    target = TargetState(1)
    target.position = [t * t * ramp_acc]
    target.velocity = [t * ramp_acc]
    target.acceleration = [ramp_acc]
    return target
 
def model_sinus(t, ramp_vel=0.4):
    target = TargetState(1)
    target.position = [sin(ramp_vel * t)]
    target.velocity = [ramp_vel * cos(ramp_vel * t)]
    target.acceleration = [-ramp_vel * ramp_vel * sin(ramp_vel * t)]
    return target
 
 
if __name__ == '__main__':
    inp = InputParameter(1)
    out = OutputParameter(inp.degrees_of_freedom)
    otg = Trackig(inp.degrees_of_freedom, 0.01)
 
    inp.current_position = [0.0]
    inp.current_velocity = [0.0]
    inp.current_acceleration = [0.0]
 
    inp.max_velocity = [0.8]
    inp.max_acceleration = [2.0]
    inp.max_jerk = [5.0]
 
    # Optional minimum and maximum position
    inp.min_position = [-2.5]
    inp.max_position = [2.5]
 
    # otg.reactiveness = 1.0 # default value, should be in [0, 1]
 
    print('\t'.join(['t'] + [str(i) for i in range(otg.degrees_of_freedom)]))
 
    steps, target_list, follow_list = [], [], []
    for t in range(500):
        target_state = model_ramp(otg.delta_time * t)
 
        steps.append(t)
        res = otg.update(target_state, inp, out)
 
        out.pass_to_input(inp)
 
        print('\t'.join([f'{p:0.3f}' for p in target_state.position] + [f'{p:0.3f}' for p in out.new_position]) + f' in {out.calculation_duration:0.2f} [µs]')
 
        target_list.append([target_state.position, target_state.velocity, target_state.acceleration])
        follow_list.append([out.new_position, out.new_velocity, out.new_acceleration])
 
 
    # Plot the trajectory
    # import numpy as np
    # import matplotlib.pyplot as plt
 
    # follow_list = np.array(follow_list)
    # target_list = np.array(target_list)
 
    # plt.ylabel(f'DoF 1')
    # plt.plot(steps, follow_list[:, 0], label='Follow Position')
    # plt.plot(steps, follow_list[:, 1], label='Follow Velocity', linestyle='dotted')
    # plt.plot(steps, follow_list[:, 2], label='Follow Acceleration', linestyle='dotted')
    # plt.plot(steps, target_list[:, 0], color='r', label='Target Position')
    # plt.grid(True)
    # plt.legend()
 
    # plt.savefig(Path(__file__).parent.absolute() / '13_trajectory.pdf')

Output Trajectory