GPD: Guided Polynomial Diffusion for Motion Planning

Ajit Srikanth*¹    Parth Mahanjan*¹    Kallol Saha*²    Vishal Mandadi*¹    Pranjal Paul†¹    Pawan Wadhwani†¹    Brojeshwar Bhowmick³    Arun Singh⁴    K Madhava Krishna¹   

¹ Robotics Research Center, IIIT Hyderabad, India    ² Carnegie Mellon University    ³ TCS Research    ⁴ University of Tartu   

Diffusion-based motion planners are becoming popular due to their well-established performance improve-ments, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary limitation of the diffusion process is the requirement for a substantial number of denoising steps, especially when the denoising process is coupled with gradient-based guidance.In this paper, we introduce, for the first time, diffusion in the parametric space of trajectories, where the parameters are represented as Bernstein coefficients. We show that this representation greatly improves the effectiveness of the cost-function guidance and the inference speed. We also introduce a novel stitching algorithm that leverages the diversity in diffusion-generated trajectories to produce collision-free tra-jectories with just a single cost function-guided model. We demonstrate that our approaches outperform current SOTA diffusion-based motion planners for manipulators and provide an ablation study on key components.