Geometric Projectors: Geometric Constraints based Optimization for Robot Behaviors

Xuemin Chi, Tobias Löw, Yiming Li, Zhitao Liu and Sylvain Calinon

arXiv:2309.08802, 2023



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.


      title={Geometric Projectors: Geometric Constraints based Optimization for Robot Behaviors}, 
      author={Xuemin Chi and Tobias Löw and Yiming Li and Zhitao Liu and Sylvain Calinon},