Geometric Projectors: Geometric Constraints based Optimization for Robot Behaviors
Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot’s own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new framework based on Geometric Projectors (GeoPro) for constrained optimization. This novel framework allows for the generation of task-agnostic behaviors that are compliant with geometric constraints. GeoPro streamlines the design of behaviors in both task and configuration spaces, offering diverse functionalities such as collision avoidance and goal-reaching, while maintaining high computational efficiency. We validate the efficacy of our work through simulations and Franka Emika robotic experiments, comparing its performance against state-of-the-art methodologies. This comprehensive evaluation highlights GeoPro's versatility in accommodating robots with varying dynamics and precise geometric shapes.
Shape Behaviors
Base behavior
Safe behavior
Safe behavior
Boundary limits
Consistent convergence
Shared safety behavior
Safety-ware behavior
Implicit goals
Implicit goals
Subgoals
Non-holonomic Systems
Inverse Kinematics
End-effector: triangle
Object: pentagon
End-effector: rectangle
Object: triangle
End-effector: L shape
Object: Square
End-effector: quadrilateral
Object: triangle
Planar Arm
Straight line behavior
Orientation constraint
Exploration behavior
Orientation constraint
Remain a constant distance
Object centers oriented
Collision free insertion task
Autonomous Parking
Parallel Parking
Perpendicular Parking
Franka Emika Insertion Task Experiments
