FOCI: Trajectory Optimization on Gaussian Splats

3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes FOCI (Field Overlap Collision Integral), an algorithm that is able to optimize trajectories directly on the Gaussians themselves. FOCI leverages a novel and interpretable collision formulation for 3DGS using the notion of the overlap integral between Gaussians. Contrary to other approaches, which represent the robot with conservative bounding boxes that underestimate the traversability of the environment, we propose to represent the environment and the robot as Gaussian Splats. This not only has desirable computational properties, but also allows for orientation-aware planning, allowing the robot to pass through very tight and narrow spaces. We extensively test our algorithm in both synthetic and real Gaussian Splats, showcasing that collision-free trajectories for the ANYmal legged robot that can be computed in a few seconds, even with hundreds of thousands of Gaussians making up the environment. The project page and code are available at https://rffr.leggedrobotics.com/works/foci/

Beyond the Cascade: Juggling Vanilla Siteswap Patterns

Being widespread in human motor behavior, dynamic movements demonstrate higher efficiency and greater capacity to address a broader range of skill domains compared to their quasi-static counterparts. Among the frequently studied dynamic manipulation problems, robotic juggling tasks stand out due to their inherent ability to scale their difficulty levels to arbitrary extents, making them an excellent subject for investigation. In this study, we explore juggling patterns with mixed throw heights, following the vanilla siteswap juggling notation, which jugglers widely adopted to describe toss juggling patterns. This requires extending our previous analysis of the simpler cascade juggling task by a throw-height sequence planner and further constraints on the end effector trajectory. These are not necessary for cascade patterns but are vital to achieving patterns with mixed throw heights. Using a simulated environment, we demonstrate successful juggling of most common 3-9 ball siteswap patterns up to 9 ball height, transitions between these patterns, and random sequences covering all possible vanilla siteswap patterns with throws between 2 and 9 ball height. https://kai-ploeger.com/beyond-cascades