  For many robotic manipulation and contact tasks, it is crucial to accurately
estimate uncertain object poses, for which certain geometry and sensor
information are fused in some optimal fashion. Previous results for this
problem primarily adopt sampling-based or end-to-end learning methods, which
yet often suffer from the issues of efficiency and generalizability. In this
paper, we propose a novel differentiable framework for this uncertain pose
estimation during contact, so that it can be solved in an efficient and
accurate manner with gradient-based solver. To achieve this, we introduce a new
geometric definition that is highly adaptable and capable of providing
differentiable contact features. Then we approach the problem from a bi-level
perspective and utilize the gradient of these contact features along with
differentiable optimization to efficiently solve for the uncertain pose.
Several scenarios are implemented to demonstrate how the proposed framework can
improve existing methods.
