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Prespecified-Performance Kinematic Tracking Control for Aerial Manipulation

Huazi Cao, Jiahao Shen, Zhengzhen Li, Qinquan Ren, Shiyu Zhao

TL;DR

Prespecified-Performance Kinematic Tracking Control for Aerial Manipulation addresses end-effector tracking for a quadcopter-Delta arm system under a preset completion time $t_p$ and a defined performance envelope $\bm{\rho}(t)$. The method fuses a preset-trajectory tracking component with a quadratic-programming (QP) based reference allocation to compute feasible base and arm references that honor physical limits; the tracking layer uses a preset error trajectory $\bm{\alpha}(t)$ and a sliding-like vector $\bm{s}=\bm{z}+\bm{\Lambda}\int\bm{z}dt$ with $\bm{z}=\bm{e}_E-\bm{\alpha}(t)$. Key contributions include (i) a two-layer architecture enabling convergence within $t_p$ while staying in $\bm{\rho}(t)$, (ii) a performance-envelope design method linking $\bm{\rho}_0$, $\bm{\rho}_\infty$, and $l_E$ to task metrics, (iii) the QP-based reference allocation that accounts for position, velocity, and acceleration limits via OSQP, and (iv) validation through static point tracking, aerial grasping, and peg-in-hole experiments showing reduced terminal errors and guaranteed preset-time completion.

Abstract

This paper studies the kinematic tracking control problem for aerial manipulators. Existing kinematic tracking control methods, which typically employ proportional-derivative feedback or tracking-error-based feedback strategies, may fail to achieve tracking objectives within specified time constraints. To address this limitation, we propose a novel control framework comprising two key components: end-effector tracking control based on a user-defined preset trajectory and quadratic programming-based reference allocation. Compared with state-of-the-art approaches, the proposed method has several attractive features. First, it ensures that the end-effector reaches the desired position within a preset time while keeping the tracking error within a performance envelope that reflects task requirements. Second, quadratic programming is employed to allocate the references of the quadcopter base and the Delta arm, while considering the physical constraints of the aerial manipulator, thus preventing solutions that may violate physical limitations. The proposed approach is validated through three experiments. Experimental results demonstrate the effectiveness of the proposed algorithm and its capability to guarantee that the target position is reached within the preset time.

Prespecified-Performance Kinematic Tracking Control for Aerial Manipulation

TL;DR

Prespecified-Performance Kinematic Tracking Control for Aerial Manipulation addresses end-effector tracking for a quadcopter-Delta arm system under a preset completion time and a defined performance envelope . The method fuses a preset-trajectory tracking component with a quadratic-programming (QP) based reference allocation to compute feasible base and arm references that honor physical limits; the tracking layer uses a preset error trajectory and a sliding-like vector with . Key contributions include (i) a two-layer architecture enabling convergence within while staying in , (ii) a performance-envelope design method linking , , and to task metrics, (iii) the QP-based reference allocation that accounts for position, velocity, and acceleration limits via OSQP, and (iv) validation through static point tracking, aerial grasping, and peg-in-hole experiments showing reduced terminal errors and guaranteed preset-time completion.

Abstract

This paper studies the kinematic tracking control problem for aerial manipulators. Existing kinematic tracking control methods, which typically employ proportional-derivative feedback or tracking-error-based feedback strategies, may fail to achieve tracking objectives within specified time constraints. To address this limitation, we propose a novel control framework comprising two key components: end-effector tracking control based on a user-defined preset trajectory and quadratic programming-based reference allocation. Compared with state-of-the-art approaches, the proposed method has several attractive features. First, it ensures that the end-effector reaches the desired position within a preset time while keeping the tracking error within a performance envelope that reflects task requirements. Second, quadratic programming is employed to allocate the references of the quadcopter base and the Delta arm, while considering the physical constraints of the aerial manipulator, thus preventing solutions that may violate physical limitations. The proposed approach is validated through three experiments. Experimental results demonstrate the effectiveness of the proposed algorithm and its capability to guarantee that the target position is reached within the preset time.

Paper Structure

This paper contains 14 sections, 2 theorems, 23 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Modeling
  3. Coordinate Frames and Notations
  4. Kinematics of the Aerial Manipulator
  5. Preset Trajectory Tracking Control
  6. Performance Envelope
  7. Preset Tracking Error Trajectory
  8. Tracking Control Design
  9. Reference Allocation
  10. Experimental Verification
  11. Example 1: Static Point Tracking
  12. Example 2: Aerial Grasping
  13. Example 3: Peg-in-hole Assembly
  14. Conclusion

Key Result

Lemma 1

Let $\varepsilon_{\nu}$ be a positive constant satisfying $\varepsilon_{\nu} <\min\{\rho_{\nu,\infty}, \rho_{\nu,0}-|e_{E,\nu}(0)|\}$, where $\nu\in\{ x,y,z\}$. For the preset trajectory of the tracking error calculated by eq_alpha, if $c_{\nu}>b_{\nu}/(\rho_{\nu,0}-\varepsilon_{\nu} -|e_{E, \nu}(0)

Figures (5)

  • Figure 1: Aerial peg-in-hole assembly by an aerial manipulator. Details are available in the supplementary video.
  • Figure 2: The system overview, the preset envelope, and experimental setup of the aerial manipulator system.
  • Figure 3: Experiment results of the static point tracking example.
  • Figure 4: Experiment results of the aerial grasping example.
  • Figure 5: Experiment results of the peg-in-hole assembly example.

Theorems & Definitions (2)

  • Lemma 1: shi2024apreset
  • Theorem 1