Trajectory Generation and Control in Operational Space

This project concerns the planning and execution of end-effector trajectories for a 7-DOF robotic manipulator within a ROS and Gazebo simulation environment. The control framework is based on the Kinematics and Dynamics Library (KDL), which provides forward/inverse kinematics, Jacobians, and dynamic model computation. The work extends an existing ROS control package designed for manipulators.

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Overview

The objective is to guide the end-effector of the robot along predefined spatial paths while regulating motion dynamics. Two types of trajectories were considered:

• Linear paths, defined between two distinct Cartesian poses.
• Circular paths, defined in the vertical plane passing through the initial end-effector position.

For both trajectory types, the evolution along the path is parameterized using a curvilinear progress variable ranging between start and end states.

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Motion Profiles

Two different time laws were implemented to govern how the progress variable evolves:

1. Trapezoidal velocity profile, ensuring bounded acceleration and velocity during motion.
2. Cubic polynomial profile, enforcing zero initial and final velocity and acceleration.

These profiles influence smoothness, dynamic demand, and control effort during movement.

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Control Framework

Trajectory execution is handled through an inverse dynamics controller. The controller uses:

• The robot’s inertia matrix, Coriolis contributions, and gravity terms.
• The geometric Jacobian to map quantities between joint and task spaces.

Two control strategies were applied:

Approach	Control Domain	Error Feedback	Use Case
Joint-space inverse dynamics	Joint coordinates	Difference in joint states	Tracking predefined trajectories in configuration space
Operational-space inverse dynamics	Cartesian coordinates	Difference in end-effector pose and twist	Direct control of the end-effector in task space

In the operational-space formulation, the Cartesian stiffness and damping behavior is regulated directly, while internal joint dynamics are handled through projectors that preserve redundancy.

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Simulation and Evaluation

• All tests were performed in Gazebo, using ROS controllers interfaced through the standard control manager.
• End-effector motion was visualized to validate geometric correctness of linear and circular paths.
• Joint torques were recorded by streaming effort commands and logging them into a bag file.
• Logged data were analyzed in MATLAB to assess smoothness and transient response.
• Controller gains were adjusted based on these plots to obtain stable and non-oscillatory behavior.

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Software Dependencies

• ROS (with real-time controller manager)
• Gazebo
• KDL (Kinematics and Dynamics Library)
• Standard ROS packages for the KUKA iiwa manipulator
• MATLAB (optional, for post-processing of recorded torque data)

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Repository Structure

src/
├─ Trajectory planning module (path and profile generation)
├─ Control module (inverse dynamics in joint and operational space)
└─ Test node (execution of trajectories in Gazebo)

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Demo Video

Circular Trajectory - Cubic Polynomial velocity profile

cubic_polinomial_circular_front.mp4

Linear Trajectory - Trapezoidal velocity profile

trapeziodal_linear_above.mp4