DecompGrind: A Decomposition Framework for Robotic Grinding via Cutting-Surface Planning and Contact-Force Adaptation

Abstract

Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging because removal resistance varies with local contact conditions. Moreover, it is difficult to achieve accurate estimation of removal resistance and analytical modeling of shape transition, and learning-based approaches often require large amounts of training data to cover diverse processing conditions. To address these challenges, we decompose robotic grinding into two components: removal-shape planning and contact-force adaptation. Based on this formulation, we propose DecompGrind, a framework that combines Global Cutting-Surface Planning (GCSP) and Local Contact-Force Adaptation (LCFA). GCSP determines removal shapes through geometric analysis of the current and target shapes without learning, while LCFA learns a contact-force adaptation policy using bilateral control-based imitation learning during the grinding of each removal shape. This decomposition restricts learning to local contact-force adaptation, allowing the policy to be learned from a small number of demonstrations, while handling global shape transition geometrically. Experiments using a robotic grinding system and 3D-printed workpieces demonstrate efficient robotic grinding of workpieces having different shapes and material hardness while maintaining safe levels of contact force.

Figures (9)

• Figure 1: Overview of robotic grinding for object shaping with DecompGrind framework. This framework grinds the workpiece into the target shape while considering removal resistance. DecompGrind consists of Global Cutting-Surface Planning (GCSP) and Local Contact-Force Adaptation (LCFA). GCSP is used to plan the next removal shape from the current shape, and LCFA is implemented for grinding each decomposed removal shape with appropriate contact force.
• Figure 2: Cutting-surface model. The current shape $\mathbf{O}_k$ is divided into a next shape $\mathbf{O}_{k+1}^{\mathrm{Geom}}$ and a removal shape $\mathbf{r}_{k+1}^{\mathrm{Geom}}$ using the cutting surface as a geometric boundary. Here, the superscript $\mathrm{Geom}$ indicates a geometry-based representation.
• Figure 3: Framework of Bilateral Control-based Imitation Learning (BCIL). Demonstration: A demonstrator operates the leader robot while the follower robot executes the task via bilateral control, and the robot states are recorded as training data. Training: Using the collected training data, the policy is trained to predict the next leader state from the current follower state. The predicted next leader state is denoted by $\hat{\mathbf{z}}_{t+1}^{l}$. Execution: The learned policy substitutes for the leader in bilateral control. The follower robot performs the task accordingly. The policy reproduces the demonstrator’s contact behavior to regulate contact force.
• Figure 4: Framework of DecompGrind. A cutting surface is planned from the current and target shapes. The robot is then set up at the initial position based on the planned cutting surface. Next, the learned LCFA is then used to grind the removal shape defined by GCSP. Grinding continues until the contact surface $\mathbf{c}_t^{\mathrm{con}}$ reaches the cutting surface $\mathbf{c}_k^*$. Here, $\mathbf{c}_t^{\mathrm{con}}$ denotes the contact surface between the belt and the workpiece, $\mathbf{c}_k$ denotes a candidate cutting surface, and $\mathbf{c}_k^*$ denotes the selected optimal cutting surface. When $\|\mathbf{c}_t^\mathrm{con}-\mathbf{c}_k^*\|<\epsilon$, the current shape is observed and the next cutting surface is planned. Here, $\epsilon>0$ is a small positive constant. The index $k$ denotes the update step of GCSP and $t$ denotes the time step of LCFA. The functions $\Gamma_{\mathrm{sur}}(\cdot)$ and $\Gamma_{\mathrm{sur}}^{-1}(\cdot)$ represent the conversion between the robot state and the surface representation.
• Figure 5: Configuration of grinding environment. The experimental setup consists of a leader-follower robot system connected via bilateral control. The workpiece is attached to the follower end-effector and observed with a 3D vision sensor. During the demonstration phase, the demonstrator manipulates the leader robot under contact-force feedback from the environment, and the follower robot performs grinding through bilateral control. In the execution phase, the follower robot performs grinding based on the policy learned via BCIL, without using the leader robot.