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Safety Filter Design for Articulated Frame Steering Vehicles In the Presence of Actuator Dynamics Using High-Order Control Barrier Functions

Naeim Ebrahimi Toulkani, Reza Ghabcheloo

Abstract

Articulated Frame Steering (AFS) vehicles are widely used in heavy-duty industries, where they often operate near operators and laborers. Therefore, designing safe controllers for AFS vehicles is essential. In this paper, we develop a Quadratic Program (QP)-based safety filter that ensures feasibility for AFS vehicles with affine actuator dynamics. To achieve this, we first derive the general equations of motion for AFS vehicles, incorporating affine actuator dynamics. We then introduce a novel High-Order Control Barrier Function (HOCBF) candidate with equal relative degrees for both system controls. Finally, we design a Parametric Adaptive HOCBF (PACBF) and an always-feasible, QP-based safety filter. Numerical simulations of AFS vehicle kinematics demonstrate the effectiveness of our approach.

Safety Filter Design for Articulated Frame Steering Vehicles In the Presence of Actuator Dynamics Using High-Order Control Barrier Functions

Abstract

Articulated Frame Steering (AFS) vehicles are widely used in heavy-duty industries, where they often operate near operators and laborers. Therefore, designing safe controllers for AFS vehicles is essential. In this paper, we develop a Quadratic Program (QP)-based safety filter that ensures feasibility for AFS vehicles with affine actuator dynamics. To achieve this, we first derive the general equations of motion for AFS vehicles, incorporating affine actuator dynamics. We then introduce a novel High-Order Control Barrier Function (HOCBF) candidate with equal relative degrees for both system controls. Finally, we design a Parametric Adaptive HOCBF (PACBF) and an always-feasible, QP-based safety filter. Numerical simulations of AFS vehicle kinematics demonstrate the effectiveness of our approach.

Paper Structure

This paper contains 13 sections, 2 theorems, 41 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries and Problem Formulation
  4. High Order Control Barrier Functions (HOCBF)
  5. Parameter adaptive HOCBFs (PACBFs)
  6. Kinematic Model of an AFS Vehicle
  7. Methodology
  8. Goal-Reaching Controller Design for AFS Vehicles
  9. AFS Vehicles with Affine Actuator Dynamics
  10. Proposing an HOCBF Candidate for AFS Vehicles
  11. Designing a PACBF-Based Safety Filter for AFS Vehicles
  12. Simulation and Results
  13. Conclusion

Key Result

Theorem 1

Let $h: \mathbb{R}^{n_x} \to \mathbb{R}$ be an HOCBF as defined in Definition definition: HOCBF. If $\boldsymbol{x} \in \mathcal{C}_1 \cap \dots \cap \mathcal{C}_m$, then any Lipschitz continuous controller $\boldsymbol{u} \in \mathcal{U}$ that satisfies eq:HOCBF renders the set $\mathcal{C}_1 \cap

Figures (6)

  • Figure 1: Safe goal reaching mission for an AFS vehicle considering actuator dynamics using our PACBF-based safety filter.
  • Figure 2: Schematic of an AFS vehicle and its relative pose to the goal point and an example obstacle
  • Figure 3: (a) Effect of formulating safety with $h_1(\boldsymbol{z}) \geq 0$ for different values of $\eta$; (b) Comparison of $h_2(\boldsymbol{z})$ with naively adding a safe distance, $d_{min}$, to the obstacle radius in $h_1(\boldsymbol{z})$.
  • Figure 4: Nominal, command, and actual control input trajectories.
  • Figure 5: Penalty functions $p_1(t)$ and $p_2(t)$, and dynamics of $\nu_1$.
  • ...and 1 more figures

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5: Control Lyapunov Functions (CLF) ames2012control
  • Definition 6
  • Theorem 1
  • Remark 1
  • Theorem 2