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Nonparametric adaptive payload tracking for an offshore crane

Torbjørn Smith, Olav Egeland

TL;DR

The paper tackles payload tracking for offshore cranes under unknown disturbances by introducing a Cartesian load-dynamics model and a partial feedback linearization controller. It integrates a nonparametric adaptive controller based on reproducing kernel Hilbert spaces to approximate unknown disturbance forces, with an adaptive law that guarantees uniformly ultimately bounded tracking errors under probabilistic conditions. A deadzone and saturation mechanism is added to the adaptation to handle noise and approximation error, preserving stability with a controllable ultimate bound. Validation via simulations and experiments (including a KUKA robotic surrogate) shows that the Cartesian formulation yields dramatically improved tracking over angular formulations, and the nonparametric adaptive controller achieves substantial error reductions (up to ~86–82% depending on scenario), signaling strong practical potential for offshore crane operation safety and efficiency.

Abstract

A nonparametric adaptive controller is proposed for crane control where the payload tracks a desired trajectory with feedback from the payload position. The controller is based on a novel version of partial feedback linearization where the unactuated crane load dynamics are controlled with the position of the actuated crane dynamics instead of the acceleration. This is made possible by taking advantage of the gravity terms in a new Cartesian model that we propose for the load dynamics. This Cartesian model structure makes it possible to implement a nonparametric adaptive controller which cancels disturbances on the crane load by approximating the effects of unknown disturbance forces and structurally unknown dynamics in a reproducing kernel Hilbert space (RKHS). It is shown that the nonparametric adaptive controller leads to uniformly ultimately bounded errors in the presence of unknown forces and unmodeled dynamics. In addition, it is shown that the proposed partial feedback linearization based on the Cartesian model has certain advantages in payload tracking control also in the non-adaptive case. The performance of the nonparametric adaptive controller is validated in simulation and experiments with good results.

Nonparametric adaptive payload tracking for an offshore crane

TL;DR

The paper tackles payload tracking for offshore cranes under unknown disturbances by introducing a Cartesian load-dynamics model and a partial feedback linearization controller. It integrates a nonparametric adaptive controller based on reproducing kernel Hilbert spaces to approximate unknown disturbance forces, with an adaptive law that guarantees uniformly ultimately bounded tracking errors under probabilistic conditions. A deadzone and saturation mechanism is added to the adaptation to handle noise and approximation error, preserving stability with a controllable ultimate bound. Validation via simulations and experiments (including a KUKA robotic surrogate) shows that the Cartesian formulation yields dramatically improved tracking over angular formulations, and the nonparametric adaptive controller achieves substantial error reductions (up to ~86–82% depending on scenario), signaling strong practical potential for offshore crane operation safety and efficiency.

Abstract

A nonparametric adaptive controller is proposed for crane control where the payload tracks a desired trajectory with feedback from the payload position. The controller is based on a novel version of partial feedback linearization where the unactuated crane load dynamics are controlled with the position of the actuated crane dynamics instead of the acceleration. This is made possible by taking advantage of the gravity terms in a new Cartesian model that we propose for the load dynamics. This Cartesian model structure makes it possible to implement a nonparametric adaptive controller which cancels disturbances on the crane load by approximating the effects of unknown disturbance forces and structurally unknown dynamics in a reproducing kernel Hilbert space (RKHS). It is shown that the nonparametric adaptive controller leads to uniformly ultimately bounded errors in the presence of unknown forces and unmodeled dynamics. In addition, it is shown that the proposed partial feedback linearization based on the Cartesian model has certain advantages in payload tracking control also in the non-adaptive case. The performance of the nonparametric adaptive controller is validated in simulation and experiments with good results.

Paper Structure

This paper contains 8 sections, 3 theorems, 20 equations, 19 figures, 9 tables.

Table of Contents

  1. Adaptive control
  2. Adaption with deadzone and saturation
  3. Experiments
  4. Comparison of angular and Cartesian formulation
  5. Simulations and experiments with the nonparametric adaptive controller
  6. Simulation study
  7. Experimental validation
  8. Conclusion

Key Result

Proposition 4.3

The nominal error dynamics are exponentially stable and admit a Lyapunov function $Q({\bm{e}})$ so that $\nabla Q({\bm{e}})$ is locally bounded in ${\bm{e}}$ and locally Lipschitz in ${\bm{e}}$, $\nabla Q({\bm{e}})^{\text{T}}{\bm f}_e({\bm{e}}) \leq -k_Q\|{\bm{e}}\|_2^2$ and $k_1\|{\bm{e}}\|_2^2\leq Q({\bm{e}})\leq k_2\|{\bm{

Figures (19)

  • Figure 2: Model of the crane system showing the main components of the test setup and notation used to present the results.
  • Figure 3: Reference trajectory that was used in simulations for comparison of the Cartesian and angular controllers
  • Figure 4: Angular controller tracking performance
  • Figure 5: Cartesian controller tracking performance
  • Figure 6: Position control error ${e_x}$ and ${e_y}$ for angular controller
  • ...and 14 more figures

Theorems & Definitions (3)

  • Proposition 4.3
  • Theorem 4.4
  • Theorem 4.5