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The task of “relative placement” is to predict the placement of one object in relation to another, e.g. placing a mug onto a mug rack. Through explicit object-centric geometric reasoning, recent methods for relative placement have made tremendous progress towards data-efficient learning for robot manipulation while generalizing to unseen task variations. However, they have yet to represent deformable transformations, despite the ubiquity of non-rigid bodies in real world settings. As a first step towards bridging this gap, we propose “cross-displacement” - an extension of the principles of relative placement to geometric relationships between deformable objects - and present a novel vision-based method to learn cross-displacement through dense diffusion. To this end, we demonstrate our method’s ability to generalize to unseen object instances, out- of-distribution scene configurations, and multimodal goals on multiple highly deformable tasks (both in simulation and in the real world) beyond the scope of prior works. 

Safe path planning is critical for bipedal robots to operate in safety-critical environments. Common path planning algorithms, such as RRT or RRT*, typically use geometric or kinematic collision check algorithms to ensure collision-free paths toward the target position. However, such approaches may generate non-smooth paths that do not comply with the dynamics constraints of walking robots. It has been shown that the control barrier function (CBF) can be integrated with RRT/RRT* to synthesize dynamically feasible collision-free paths. Yet, existing work has been limited to simple circular or elliptical shape obstacles due to the challenging nature of constructing appropriate barrier functions to represent irregularly shaped obstacles. In this paper, we present a CBF-based RRT* algorithm for bipedal robots to generate a collision-free path through space with multiple polynomial-shaped obstacles. In particular, we used logistic regression to construct polynomial barrier functions from a grid map of the environment to represent irregularly shaped obstacles. Moreover, we developed a multi-step CBF steering controller to ensure the efficiency of free space exploration. The proposed approach was first validated in simulation for a differential drive model, and then experimentally evaluated with a 3D humanoid robot, Digit, in a lab setting with randomly placed obstacles.