Introduction

This project contains Python 3 scripts that plans a trajectory for the end-effector of the youBot mobile manipulator, performs odometry as the chassis moves, and performs feedback control to drive the youBot to pick up a block at a specified position and deliver it to the desired location in the CoppeliaSim simulation. The source codes can be found in the following link:

https://github.com/rubberdk/KUKA-youbot-Manipulation

RESULTS

CODES

There are a total 4 Python scripts which are milestone1:NextState, milestone2:TrajectoryGenerator, milestone3:FeedforwardControl, and Run. Three milestones define functions that manipulate the configuration of the robot, and the Run script combines those three functions, plot Xerr, and generates a csv file that can be used in the CoppeliaSim simulation.

Milestone 1: NextState

The main function in the simulator, called NextState takes

Inputs:

● 12-vector representing the current configuration of the robot

● 9-vector of controls indicating the arm joint speeds

● timestep Δt

● positive real value indicating the maximum angular speed of the arm joints and the wheels.

Outputs:

● new arm joint angles = (old arm joint angles) + (joint speeds) * Δt

● new wheel angles = (old wheel angles) + (wheel speeds) * Δt

● new chassis configuration is obtained from odometry

Milestone 2: TrajectoryGenerator

TrajectoryGenerator generates the reference trajectory for the end-effector frame {e}. It takes

Inputs: ● The initial configuration of the end-effector in the reference trajectory: ​ T ​ se , ​ initial​ .

● The cube’s initial configuration: ​ T ​ sc ​ ,initial​ .

● The cube’s desired final configuration: ​ T ​ sc ​ ,final​ .

● The end-effector’s configuration relative to the cube when it is grasping the cube: ​ T ​ ce ​ ,grasp​ .

● The end-effector’s standoff configuration above the cube, before and after grasping, relative to the cube

● The number of trajectory reference configurations per dt seconds

Output:

● A representation of the ​ N ​ configurations of the end-effector along the entire concatenated eight-segment reference trajectory.

Milestone 3: FeedbackControl

This function calculates the kinematic task-space feedforward plus feedback control law taking

Inputs:

● The current actual end-effector configuration X (also written Tse).

● he current end-effector reference configuration Xd (i.e., Tse,d).

● The end-effector reference configuration at the next time step in the reference trajectory, Xd,next

● The PI gain matrices Kp and Ki.

● The timestep Δt between reference trajectory configurations.

Output:

● The commanded end-effector twist expressed in the end-effector frame {e}.

Run

This script combines three functions above and executes a function called run which plots Xerr and generates a csv file for the CoppeliaSim animation and log file.