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Robust Dynamic Control Barrier Function Based Trajectory Planning for Mobile Manipulator

Lihao Xu, Xiaogang Xiong, Bai Yang, Yunjiang Lou

TL;DR

The paper tackles safe, real-time trajectory planning for high-dimensional mobile manipulators in dynamic environments with external disturbances and measurement errors. It introduces Robust Dynamic Control Barrier Function (RDCBF) by coupling Dynamic Control Barrier Functions with a Disturbance Observer to maintain safety while handling dynamic obstacles and uncertain environment information. It provides analytic geometric distance computations (segment-to-segment, segment-to-rectangle) and a cuboid bounding-box to enable accurate obstacle constraints, and demonstrates real-time performance on an 8-DoF manipulator across two scenarios, outperforming APF, MPC, and baseline CBF approaches in safety and efficiency. The work advances robust obstacle avoidance for complex, high-dimensional robotic systems and suggests future extensions to higher-order RDCBF and hardware deployment for practical use.

Abstract

High-dimensional robot dynamic trajectory planning poses many challenges for traditional planning algorithms. Existing planning methods suffer from issues such as long computation times, limited capacity to address intricate obstacle models, and lack of consideration for external disturbances and measurement inaccuracies in these high-dimensional systems. To tackle these challenges, this paper proposes a novel trajectory planning approach that combines Dynamic Control Barrier Function (DCBF) with a disturbance observer to create a Robust Dynamic Control Barrier Function (RDCBF) planner. This approach successfully plans trajectories in environments with complex dynamic obstacles while accounting for external disturbances and measurement uncertainties, ensuring system safety and enabling precise obstacle avoidance. Experimental results on a mobile manipulator demonstrate outstanding performance of the proposed approach.

Robust Dynamic Control Barrier Function Based Trajectory Planning for Mobile Manipulator

TL;DR

The paper tackles safe, real-time trajectory planning for high-dimensional mobile manipulators in dynamic environments with external disturbances and measurement errors. It introduces Robust Dynamic Control Barrier Function (RDCBF) by coupling Dynamic Control Barrier Functions with a Disturbance Observer to maintain safety while handling dynamic obstacles and uncertain environment information. It provides analytic geometric distance computations (segment-to-segment, segment-to-rectangle) and a cuboid bounding-box to enable accurate obstacle constraints, and demonstrates real-time performance on an 8-DoF manipulator across two scenarios, outperforming APF, MPC, and baseline CBF approaches in safety and efficiency. The work advances robust obstacle avoidance for complex, high-dimensional robotic systems and suggests future extensions to higher-order RDCBF and hardware deployment for practical use.

Abstract

High-dimensional robot dynamic trajectory planning poses many challenges for traditional planning algorithms. Existing planning methods suffer from issues such as long computation times, limited capacity to address intricate obstacle models, and lack of consideration for external disturbances and measurement inaccuracies in these high-dimensional systems. To tackle these challenges, this paper proposes a novel trajectory planning approach that combines Dynamic Control Barrier Function (DCBF) with a disturbance observer to create a Robust Dynamic Control Barrier Function (RDCBF) planner. This approach successfully plans trajectories in environments with complex dynamic obstacles while accounting for external disturbances and measurement uncertainties, ensuring system safety and enabling precise obstacle avoidance. Experimental results on a mobile manipulator demonstrate outstanding performance of the proposed approach.
Paper Structure (16 sections, 1 theorem, 23 equations, 10 figures, 2 tables, 2 algorithms)

This paper contains 16 sections, 1 theorem, 23 equations, 10 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dynamic Control Barrier Function
  4. Disturbance Observer (DOB)
  5. RDCBF Design for Trajectory Planning
  6. Geometric Computing in Mobile Manipulator
  7. Segment-to-segment Distance in 3D Space
  8. Segment-to-rectangle Distance in 3D Space
  9. Bounding Box of Cuboid
  10. RDCBF Design for Mobile Manipulator
  11. Case Study
  12. Problem Statement
  13. Experiment Results
  14. Scenario A
  15. Scenario B
  16. ...and 1 more sections

Key Result

Theorem 1

Consider the dynamic safe function $h(\cdot)$ in (RDCBFforplaning), the system sysdeq and the DOB given in (DOB) with $\hat{\bm{d}}(0)=\bm{0}$. Suppose that Assumption 1 and 2 hold, and $h_0 > 0$. If there exists constants $\gamma,\alpha,\beta >0$ such that $\alpha > \frac{\gamma+\mu}{2}$, $\beta > hold true, where $L_{g_{d}}h = \frac{\partial h}{\partial \bm{x}}\bm{g}_{d}$, $\Gamma = \omega_0 +

Figures (10)

  • Figure 1: The proposed RDCBF-Based trajectory planner. It utilizes disturbance estimates and potentially inaccurate environment information. By employing RDCBF, a set of safety constraints are constructed to compensate for both uncertainties. These constraints are integrated into the input $\bm{u}_{nom}$ from the global planner. This integration allows for the generation of control commands $\bm{u}_{safe}$ that guarantee safe trajectory planning.
  • Figure 2: Elliptic level curves $\bm{L}$ and coresponding critical points $\bm{P}$.
  • Figure 3: Illustration of the three types of projections of green line segments $\bm{l}$ onto the plane containing rectangle $\bm{\mathcal{R}}$. And the red line segments $\bm{l}_c$ are the closest line segments within $\bm{\mathcal{R}}$ to $\bm{l}$.
  • Figure 4: Bounding Box for Cuboid.
  • Figure 5: Vertical view of cuboid $\bm{\mathcal{R}}_1$ and rectangle $\bm{\mathcal{R}}_2$.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof