Calculate Jacobian for arm
机械工程代考 In addition to standard Matlab functions, your code may assume that you have access to the functions you created in previous
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Use the vector and rotation functions you created above to find the Jacobians for the endpoints of the links in a planar arm.
In addition to standard Matlab functions, your code may assume that you have access to the functions you created in previous assignments (some of these you will call directly in this assignment, some will only be called by other functions that you call). Remember that for these functions, the grading script will use the instructor's copy of the functions: 机械工程代考
- vector_set_rotate
- vector_set_cumulative_sum
- vector_set_difference
- rotation_set_cumulative_product
- threeD_rotation_set
- threeD_robot_arm_endpoints
- threeD_joint_axis_set
- Rz
- Ry
- Rx 机械工程代考
Function
function [J,...link_ends,...
link_end_set,...
link_end_set_with_base,...
v_diff,...
joint_axis_vectors,...
joint_axis_vectors_R,...
R_links] = arm_Jacobian(link_vectors,joint_angles,joint_axes,link_number) 机械工程代考
% Construct a Jacobian for a chain of links as a function of the link
% vectors, the joint angles, joint axes, and the number of the link whose
% endpoint is the location where the Jacobian is evaluated
%
% Inputs:
%
% link_vectors: A 1xn cell array in which each entry is a 3x1 link vector
% joint_angles: a nx1 vector, each element of which is the joint angle
% preceeding the corresponding link
% joint_axes: a nx1 cell array, each entry of which is 'x','y', or 'z', 机械工程代考
% designating the axis of the corresponding joint
% link_number: The number of the link whose Jacobian we want to evaluate
%
% Output:
%
% J: The Jacobian for the end of link 'link_number', with respect to
% *all* joint angles (All columns of J corresponding to joints after
% the link should be zeros)
%
% Additional outputs (These are intermediate variables. Having the option 机械工程代考
% to return them as outputs lets our automatic code checker tell you
% where problems are in your code. Some may also be useful in later
% functions):
%
% link_end_set_with_base: The endpoints of the links after taking the cumulative
% sum of link vectors, with a zero point added at the beginning
% v_diff: The set of vectors from all points in 'link_end_set_with_base' 机械工程代考
% to the end of link 'link_number'
% joint_axis_vectors: The unit vectors pointing along each joint axis in
% local coordinates
% joint_axis_vectors_R: The unit vectors pointing along each joint axis
% in world coordinates
% R_links: The orientations of the individual links 机械工程代考
% Use 'threeD_robot_arm_endpoints' to get 'link_ends', 'R_links',
% 'link_end_set' and 'link_end_set_with_base'. Note that you won't need the
% other outputs from that function, so you can write ~ for those outputs
% instead of creating a variable that you won't use
%
% For example, '[~,output_2] = f(x)' makes f(x) act as if it was asked to provide 机械工程代考
% two outputs, but only creates 'output_2'. Using this syntax makes it
% easier for Matlab's code checking to tell you if you have a bug in which
% you are forgetting to use a variable that you have defined (which
% generally means that you're using the wrong variable somewhere)
% Use 'vector_set_difference' to get the vector to the end of link 'link_number' from each
% point in link_end_set_with_base, and call it 'v_diff' 机械工程代考
% Use 'threeD_joint_axis_set' to turn the joint axes into
% a set of axis vectors called 'joint_axis_vectors'
% Use 'vector_set_rotate' to rotate the joint axes by the link
% orienations (Note that although our convention is that the ith joint
% is in the (i-1)th link, the vector associated with the joint axis is
% the same in both frame (i-1) and frame i, so we can rotate the joint
% axes directly into the corresponding frames (this means we don't have
% to offset the joint axes when calling 'vector_set_rotate'). Call the
% output of this rotation 'joint_axis_vectors_R'.
% Create a zero matrix to hold the Jacobian. It should have three rows, 机械工程代考
% and should have as many columns as there are joints
% <This piece of code doesn't affect anything yet, but will be
% important in the dynamics unit>
% Check if joint_axis_vectors_R or v_diff contain any symbolic
% variables (a cell array of symbolic variables is not itself symbolic, 机械工程代考
% so you'll need to loop over the elements, checking each one using
% isa(A,'sym'). If there are any symbolic components, then make J a
% symbolic matrix using 'J=sym(J)';
% Fill in the columns of the Jacobian. Each column is either:
%
% A. The cross product of the corresponding joint axis with the vector 机械工程代考
% from that joint location to the end of link 'link_number', or
%
% B. Zero, if the joint is after the end of link 'link_number'
%
% (Note that you can implment this conditional by making the loop that
% fills in the columns of J stop at column 'link_number')
Code to call your function 机械工程代考
%First, run with numeric input
link_vectors = {[1;0;0],[.5;0;0],[.5;0;0]};
joint_angles = [0.4;-0.5;.25]*pi;
joint_axes = {'z','z','z'};
link_number = 3; 机械工程代考
arm_Jacobian(link_vectors,joint_angles,joint_axes,link_number)
% Second, run with symbolic input
syms a b c
joint_angles = [a;b;c];
joint_axes = {'z','z','z'};
link_number = 2; 机械工程代考
arm_Jacobian(link_vectors,joint_angles,joint_axes,link_number)
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