Forward Kinematics code for robotic manipulator having any number of DOF. For a given set of link parameters and joint variables of any manipulator and the reference frame number and the tip frame number, the code outputs the concatenated homogenous transformation matrix from the reference frame to the tip frame.
The code takes the link parameter and joint varriable inputs in the form of a distal DH parameter table, where link rotation and link length are the link parameters and joint rotation (for revolute joints) and joint translation (for prismatic joints) are the joint variables.
This code also functions as the distal DH paramater to proximal DH parameter converter, where the user can get equivalent proximal DH transformation matrix for a given set of distal DH parameters. Important thing to note is that the user doesn't need to know how to construct the proximal DH table (which is quite similar to the distal DH table but a little more difficult to conceptualize) or how to assign the frames according to the proximal DH parameters. This is done as frame assignment according to distal DH parameters and constructing a distal DH table is much more widely known and used.
The distal DH parameters are to be input in a seperate text file. As an example, the human legs with one leg stanced and one leg swinging have been considered having 6 degrees of freedom. The text file where the user has to input the table is given by: dhParametersHumanLeg.txt.
Explanation of the included scripts:
1). fwdKin_robotic_manipulator.m: This is the mother script which needs to be exectuted in order run the solver. It basically parses the DH table text file and depending on the result the user wants (proximal or distal), runs the corresponding script.
2). fwdKin_RoboticManipulator_distalDH,m: this is the script which is executed by the mother script if the user needs the result according to distal DH parameters.
3). fwdKin_RoboticManipulator_proximalDH,m: this is the script which is executed by the mother script if the user needs the result according to proximal DH parameters.
4). ArmMatrix_distal.m: this is a function which is used in the fwdKin_RoboticManipulator_distalDH,m script to calculate the homogenous transformation matrix from one frame to the adjacent frame.
5). ArmMatrix_proximal.m: this is a function which is used in the fwdKin_RoboticManipulator_proximalDH,m script to calculate the homogenous transformation matrix from one frame to the adjacent frame. The variables used in the matrix for proximal DH parameters are a little different than distal DH and thus a seperate function is created. Moreover, this function performs the task of converting the input distal DH table to the equivalent proximal DH table.
6). T_Concat_distal.m: This is the function which calculates the final concatenated transformation matrix for the two input frames. This function is for the distal DH parameters.
7). T_Concat_proximal.m: This is the function which calculates the final concatenated transformation matrix for the two input frames. This function is for the proximal DH parameters.
The validation of the kinematics code is two fold: The first validation is carried out by developing a kinematic model of a augmentative lower extremity exoskeleton known as LEPES (Lower Extremity Power Assisted Exoskeleton System) developed by the Robotics lab of Beijing Forestry University, China (Yanbei Li et all, "Dynamics and Kinematic Analysis and Simulation of Lower Extremity Power-Assisted Exoskeleton", JVE International Ltd. Journal of Vibroengineering, vol. 16, no. 2, pp. 1392-8796, January, 2014). Both distal and proximal DH parameters based kinematic models of LEPES are developed and fed into the code. The configuration of LEPES is taken as following:
The following kinematic models are created:
The single support phase is taken for the configuration, with the position and orientation of the swinging leg's ankle with respect to the stanced leg's ankle is computed. The code result is compared with manual calculations using the transformation formulae given in the above referenced paper which match when the proximal calculations are used in the code.
The 2nd validation is carried out using an external marker dataset. This type of dataset is usually recorded in a gait lab where a human subject has to walk in a particular direction and form with markers attached to their body, which helps the many cameras and sensors present in the gait lab to record the movement of the subject. With the help of the movement data, a lot of information about the kinematics of gait motion can be extracted like anatomical joint angles, subject segment velocities and accelerations and joint dynamics.
Here, the markers attached to the lower limbs are taken into consideration. For each marker, its trajectory in the cartesian space is available. The human leg is modelled as a 3 link manipulator, with 3 revolute joints (hip, knee and ankle) and the base at the hip which is moving too. Only the sagittal plane movement is considered. The joint angles and link lengths are computed using the marker trajectores. The forward kinematics code is applied with the joint angles and the segment lengths as input, and the output trajectories are compared with the available marker trajectories. The 2 markers used for this validation are: Left Ankle Marker and Right Knee Marker.
Validation Structure
Validation Results
- Left Ankle X
- Left Ankle Z
- Right Knee X
- Right Knee Z
The marker trajectories and the forward kinematics calculated trajectories match, thus the code has been validated.