https://cw.fel.cvut.cz/b251/ 2026-05-03T09:36:05+0200 https://cw.fel.cvut.cz/b251/ https://cw.fel.cvut.cz/b251/lib/tpl/bulma-cw/images/favicon.ico text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw01?rev=1757938508&do=diff Homework 01 - Solving univariate polynomial equation Task Solve the problems in hw01.pdf: The given polynomials have integer roots and we want you to upload them as integers, including multiplicities.Allowed libraries Forbidden methods/classes Allowed libraries text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw02?rev=1757938508&do=diff Homework 02 - Rigid motion as a coordinate transformation Task You can find the description of the task here. For task 1: # approximate rotation R = np.array([[0.8047, -0.5059, -0.3106], [0.3106, 0.8047, -0.5059], [0.5059, 0.3106, 0.8047]]) text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw03?rev=1757938508&do=diff Homework 03 - Denavit-Hartenberg Convention Task [Motoman MA1400][dimensions][Lecture 03][here]$x$$z$ For XZ plane, you can use this snippet of code: fig = plt.figure(figsize=(10, 10)) ax = fig.add_subplot(111, projection='3d') for system in systems: plot_system(ax, system) ax.set_proj_type('ortho') ax.view_init(azim=90, elev=0) ax.set_yticklabels([]) ax.set_ylabel('') ax.set_xlim(-0.05, 1.45) ax.set_ylim(-0.75, 0.75) ax.set_zlim(-0.05, 1.45) plt.show() text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw04?rev=1757938508&do=diff Homework 04 - Forward Kinematics and Robot Workspace Forward Kinematics Implement the forward kinematic task for a general 6R manipulator. Allowed libraries Create a function fkt(mechanism, joints) which takes DH parameters of the manipulator mechanism$2$$6$$n$$n=100$$x$$y$$x$$y$ text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw05?rev=1757938508&do=diff Homework 05 - Motion Axis Task The goal of this task is to estimate joint axes of a robot from 3D point measurements. As the task description explains, we will estimate the robot motion axes by moving joints one by one and measuring the coordinates of three points fixed to the end effector of the mechanism. Two sets of variables are required to solve the task: point coordinates before the motion that are stored in $\mathbb{R}^3$$\vec{x_1}$ text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw06?rev=1757938508&do=diff Homework 06 - Rotation Interpolation In robotics, when performing tasks with a robotic arm, it is usually desired to move the end-effector of the robotic arm through a sequence of poses $(\mathbf{R}_1, \mathbf{t}_1), \dots, (\mathbf{R}_k, \mathbf{t}_k) \in \mathrm{SO}(3) \times \mathbb{R}^3$. Moreover, we want the motion from $(\mathbf{R}_j, \mathbf{t}_j)$ to $(\mathbf{R}_{j+1}, \mathbf{t}_{j+1})$ to be smooth. There are various reasons for that:$X \subseteq \mathbb{R}^n$$\mathbf{v}_0, \mathbf{… text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw07?rev=1757938508&do=diff Homework 07 - Multivariate Polynomials Allowed libraries Forbidden methods 1. Multivariate Polynomial Division Algorithm Implement the [multivariate polynomial division algorithm] for more than one divisor. Create a function poly_div(f, divs, mo) for dividing the polynomial f by the list of polynomials $$$$$G = (g_1, \dots, g_t)$$\mathbb{Q}[x_1,\dots,x_n]$$G$$\geq$$$ \overline{S_{\geq}(g_i, g_j)}^{(G, \geq)} = 0 \quad \forall i, j \in \{1,\dots,t\}, i \neq j. $$$$$$$F \subset \mathbb{Q}[x_1, … text/html 2025-09-15T14:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw08?rev=1757938508&do=diff Homework 08 - Inverse Kinematics by Newton's Method The goal of this task is to solve [the inverse kinematics of 6R manipulator using Newton's method]. Task Allowed libraries a. Implement function jac_r(mechanism, joints) that returns the rotational Jacobian for the given mechanism and its configuration joints$\boldsymbol{\theta}_0$$$\frac{\partial \mathrm{vec}(\mathbf{R})}{\partial \boldsymbol{\theta}}_{\big|\boldsymbol{\theta}_0}, \quad \text{where} \; \mathrm{vec}(\mathbf{R}) = \begin{bmat… text/html 2025-10-27T14:44:20+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/hw09?rev=1761572660&do=diff Homework 09 - Inverse Kinematics by Gröbner Basis Computation Overview The goal of this task is to solve the inverse kinematic task for a general 6R mechanism using a general Gröbner basis computation. This consists of the six main elements $\sin \alpha_i$$\cos \alpha_i$$a_i$$d_i$ Gröbner basis computation is done in exact arithmetics over rational numbers and therefore input must be provided in rational numbers. At the same time, the input must satisfy the algebraic constraints exactly, other… text/html 2025-12-07T09:16:35+0200 Anonymous (anonymous@undisclosed.example.com) https://cw.fel.cvut.cz/b251/courses/pkr/labs/start?rev=1765095395&do=diff PKR Labs Monday 12:45-14:15, CIIRC: B-670 Week Date Content Solutions Test Assignment 01 22.09 Lecture 02 29.09 Lecture 03 06.10 Test [ Test-α] Test-α 04 13.10 Rigid motion as a coordinate transformation, properties of rotation matrices, axis of motion