Plot 2D or 3D Robot Workspace

An add-on that allows plotting 2D and 3D robots' workspaces using their DH parameters

Robotic Arm Workspace Plotter

This is a Matlab add-on that allows plotting the reachable workspace 2D and 3D robotic arms using the DH parameters.

Quickstart

2D Example

Here's a basic example for plotting a 2D robot's workspace via plot2dworkspace.m:

syms theta1 theta2 theta3 real
syms d1 d2 real

% DH parameters
test_dh = [0 0 0 theta1; ...
           120 0 0 theta2; ...
           60 0 0 0]
% Parameter ranges
theta1_range = linspace(0,2*pi, 180);
theta2_range = linspace(0,2*pi, 180);
test_map = containers.Map({'theta1', 'theta2'},{theta1_range,theta2_range});

% Workspace plotting function
plot2dworkspace(test_dh, test_map)

Which will render as follows:

For more examples, see /examples.

3D Example

Here's a basic example for plotting a 3D robot's workspace via plot3dworkspace.m:

syms theta1 theta2 theta3 theta4 theta5 theta6 real
syms d1 d2 d3 d4 real

% DH parameters
test_dh = [18.5 0 42 theta1; ...
           16 pi 0 theta2; ...
           0 0 d3 0; ...
           0 0 7 theta4]
% Parameter ranges
theta1_range = arr2Rad(linspace(0,300, 50));
theta2_range = arr2Rad(linspace(0,300, 50));
d3_range = linspace(0,12, 50);
% Note the specification states 540°, but anything past 360° is redundant
theta4_range = arr2Rad(linspace(0,360, 50));
test_map = containers.Map({'theta1', 'theta2', 'd3','theta4'}, ...
    {theta1_range, theta2_range, d3_range, theta4_range}); 
% Workspace plotting function
plot3dworkspace(test_dh, test_map, @get_alternative_dh_transform)


function out = arr2Rad(A)
    out = arrayfun(@(angle) deg2rad(angle), A);
end

function T = get_alternative_dh_transform(a,alpha,d,theta)
T = [cos(theta) -cos(alpha)*sin(theta) sin(alpha)*sin(theta) a*cos(theta)
     sin(theta) cos(alpha)*cos(theta) -sin(alpha)*sin(theta) a*sin(theta)
     0 sin(alpha) cos(alpha) d
     0 0 0 1];
end

Which will render as follows:

For more examples, see /examples.

Notes

• Performance - this add-on uses a brute-force method that calculates the end-effector's position for every possible DH parameter combination. While reasonably well-optimised this can become expensive quickly. For example, if you have a 6 DOF robot and want to explore 20 possible values per parameter, this will take 20^6 = 64,000,000 operations and units of memory.
• DH Parameter Convention - there are conventions to construct the DH transformation matrix, based on the order of the individual transforms for the DH parameters. By default this add-on uses the one here, but it is possible to provide an alternative function that returns a different matrix (see above 3D example).