Bi-Level Belief Space Search for Compliant Part Mating Under Uncertainty

TL;DR

Bi-Level Belief Assembly (BILBA) addresses robust, low-clearance part mating under pose uncertainty by combining a high-level contact-sequence search with low-level compliant-motion synthesis. The method operates in belief space, using a graph of contact modes derived from configuration-space obstacle boundaries to guide stochastic compliance parameter searches, aided by Gaussian Process Regression to focus sampling. It yields open-loop conformant plans that drive a set of particles toward the desired contact while reducing uncertainty, demonstrated on simulated 3D peg-in-hole and puzzle tasks and validated on real hardware with a Franka Panda, outperforming a belief-space RRT baseline in planning efficiency and robustness. The approach enables practical assembly under uncertainty by exploiting environmental contacts through controlled stiffness and targeted gripper motions, with potential extensions to tactile/vision feedback for contingent policies.

Abstract

The problem of mating two parts with low clearance remains difficult for autonomous robots. We present bi-level belief assembly (BILBA), a model-based planner that computes a sequence of compliant motions which can leverage contact with the environment to reduce uncertainty and perform challenging assembly tasks with low clearance. Our approach is based on first deriving candidate contact schedules from the structure of the configuration space obstacle of the parts and then finding compliant motions that achieve the desired contacts. We demonstrate that BILBA can efficiently compute robust plans on multiple simulated tasks as well as a real robot rectangular peg-in-hole insertion task.

Figures (4)

• Figure 1: Let the bottom, left, and right faces of the 2D peg be denoted as "b, l, r" respectively. Similarly, let the faces of the left chamfer, right chamfer, left wall, right wall, and bottom of the hole be denoted "LC, RC, L, R, B". Our method computes a graph over pairwise contacts between faces as shown in \ref{['fig:cg']}. In \ref{['fig:cs']}, we see how the contact sequence [free, (r, RC), (b, B)], corresponds to a sequence of surfaces in the configuration space which guide the search.
• Figure 2: A sample 2D belief-space trajectory for peg-in-hole in the presence of rotational uncertainty for three particles. At each execution step, the red points correspond to the $(x, y)$ configuration of the peg for each particle. Because each particle is at a different orientation, the cross-section of $C_{\textrm{obs}}$ is slightly different. Each green dot corresponds to a setpoint generated by sampling from the surface of $C_{\textrm{obs}}$ that is obtained from the abstract contact plan. (a) Initial belief; commanded motion to gain contact with the chamfer. (b) Belief after first motion; second motion commanded to bottom of hole, compliant in the x-direction due to the normal forces generated by the surface with which the particle is in contact. (c) Final belief with all particles in desired state.
• Figure 3: Figures 3a and 3b show the "puzzle" problem in the presence of translational grasp uncertainty in the x-direction. The red, green, and blue manipulands correspond to three particles representing possible manipuland configurations. Similarly, figures 3c and 3d show the "peg" problem in the presence of rotational grasp uncertainty; the possible pitch of the peg is represented by three particles.
• Figure 4: In figure \ref{['fig:real_init']} the manipuland is held at a known configuration relative to the robot but the object position is only known to within 2cm of tolerance (as shown by the two overlaid possible object configurations). After executing the same sequence of compliant motions, the robot is able to successfully insert the peg into the hole in all the initial conditions; as shown in figure \ref{['fig:real_goal']}.