Orientation Control with Variable Stiffness Dynamical Systems

Recently, several approaches have attempted to combine motion generation and control in one loop to equip robots with reactive behaviors, that cannot be achieved with traditional time-indexed tracking controllers. These approaches however mainly focused on positions, neglecting the orientation part which can be crucial to many tasks e. g. screwing. In this work, we propose a control algorithm that adapts the robot's rotational motion and impedance in a closed-loop manner. Given a first-order Dynamical System representing an orientation motion plan and a desired rotational stiffness profile, our approach enables the robot to follow the reference motion with an interactive behavior specified by the desired stiffness, while always being aware of the current orientation, represented as a Unit Quaternion (UQ). We rely on the Lie algebra to formulate our algorithm, since unlike positions, UQ feature constraints that should be respected in the devised controller. We validate our proposed approach in multiple robot experiments, showcasing the ability of our controller to follow complex orientation profiles, react safely to perturbations, and fulfill physical interaction tasks.

Authors

• Youssef Michel
• Matteo Saveriano
• Fares J. Abu-Dakka
• Dongheui Lee

Keywords

• Tracking loops
• Tracking
• Heuristic algorithms
• Perturbation methods
• Aerospace electronics
• Behavioral sciences
• Task analysis
• System Dynamics
• Variable Stiffness
• Interactive
• Physical Interaction
• Motor Control
• Interaction Behavior
• Path Planning
• Rotational Motion
• Behavioral Reactions
• Lie Algebra
• Complex Profile
• Interaction Task
• Current Orientation
• Motion Generation
• Unit Quaternion
• Preferred Motion
• Degrees Of Freedom
• Flow Velocity
• Optimal Control
• Asymptotically Stable
• Tangent Space
• Robot Motion
• Inverse Reinforcement Learning
• Impedance Control
• Orientation Of The Robot
• Gaussian Mixture Model
• Unit Sphere
• Symmetric Behavior
• Local Magnetization
• Riemannian Manifold