Neural Configuration-Space Barriers for Manipulation Planning and Control

TL;DR

The paper tackles the problem of safe, efficient motion planning and real-time control for high-DoF robot manipulators in cluttered, dynamic environments with imperfect perception. It introduces a unified neural configuration-space distance function (CDF) barrier framework that separately learns environment-CDF $f_c$ and self-collision-CDF $f_{sc}$, and builds a neural barrier ${\hat{h}({\boldsymbol{q}}, t)}$ to certify safe regions. A bubble-based planner, called the Rapidly-Exploring Bubble Graph (RBG), leverages ${\hat{h}}$ to construct configuration-space bubbles and solve a convex Bézier-trajectory optimization, while a distributionally robust CBF (DR-CBF) controller ensures safety under dynamic obstacles and sensing/model uncertainty via a Wasserstein DRO formulation. The approach is validated on a 6-DoF xArm in both simulation and hardware, showing substantial reductions in collision checks and planning time without sacrificing path quality, and achieving high safety and tracking performance under dynamic conditions. Collectively, the framework advances practical, robust planning and control for high-DoF manipulation using onboard point-cloud observations.

Abstract

Planning and control for high-dimensional robot manipulators in cluttered, dynamic environments require both computational efficiency and robust safety guarantees. Inspired by recent advances in learning configuration-space distance functions (CDFs) as robot body representations, we propose a unified framework for motion planning and control that formulates safety constraints as CDF barriers. A CDF barrier approximates the local free configuration space, substantially reducing the number of collision-checking operations during motion planning. However, learning a CDF barrier with a neural network and relying on online sensor observations introduce uncertainties that must be considered during control synthesis. To address this, we develop a distributionally robust CDF barrier formulation for control that explicitly accounts for modeling errors and sensor noise without assuming a known underlying distribution. Simulations and hardware experiments on a 6-DoF xArm manipulator show that our neural CDF barrier formulation enables efficient planning and robust real-time safe control in cluttered and dynamic environments, relying only on onboard point-cloud observations.

Figures (5)

• Figure 1: Illustration of neural bubble-CDF planning on a planar 2-link robot arm. (a) The robot’s initial configuration (solid blue links) and two potential goal configurations (dashed red) are shown. Four obstacles with point-cloud data on their surfaces define the environment, and intermediate waypoints of the bubble-CDF planned trajectory appear in light green. (b) The 2D configuration space ($\theta_1$ vs. $\theta_2$) for a planar 2-link robot, where the color map indicates the learned CDF value (darker regions denote proximity to collision). Cyan circles represent "safe bubbles" derived from the CDF barrier, forming a graph of collision-free regions. A smooth, optimized red trajectory connects the start configuration (yellow circle) to the closest goal (red square), while another goal configuration is marked by a red triangle.
• Figure 2: Snapshots of a 2-link arm navigating a dynamic environment with purple obstacles (velocity directions shown by arrows). The arm is tasked to follow the planned path in Fig. \ref{['fig:2d_example_illustrate']}. The arm is shown in blue and the trajectory of its end-effector is shown in red, and the local reference configuration goal $\gamma(s)$ is shown in green.
• Figure 3: Bubble-CDF planning for a 6-DoF xArm robot in a static environment, targeting an end-effector goal represented by a green sphere. (a) The initial configuration of the xArm. (b, c) Intermediate configurations illustrating the planned path as the robot avoids obstacles while progressing toward the goal. (d) The final goal configuration reached by the robot.
• Figure 4: Snapshots of safe control execution on a 6-DoF xArm robot in an environment with dynamic obstacles. (a) The control execution begins at the initial configuration. (b) A dynamic obstacle (blue) approaches the robot from right. (c) The robot executes a defensive maneuver, moving upward to avoid the obstacle. (d) The robot successfully resumes tracking and reaches the goal configuration.
• Figure 5: Bubble-CDF planner and DR-CBF control applied to two real-world setups for a 6-DoF xArm robot. The top row (a-d) represents Setup 1, with the robot navigating a cluttered environment featuring a combination of static and dynamic obstacles. Similarly, the bottom row (e-h) depicts Setup 2, showcasing the planner’s adaptability in a different obstacle layout. For both setups: (a, e) illustrate the bubble-CDF planned configuration in static environments, while (b-d, f-h) demonstrate the robot's real-time adaptive responses to dynamic obstacles.