Flatness-based trajectory planning for 3D overhead cranes with friction compensation and collision avoidance

TL;DR

The paper tackles fast, collision-free trajectory planning for 3D overhead cranes that are underactuated and friction-dominated. It leverages differential flatness to transform the crane dynamics into a chain of integrators and solves a nonlinear program that minimizes $T_{END}$ while penalizing the snap via $\lambda \int_0^{T_{END}} \| r_p^{(4)}(t) \|^2 dt$, with constraints enforcing obstacle avoidance and friction effects. A comparative study contrasts three friction models (Complete Model, Simplified Model, No Dry Friction) using direct collocation in CasADi with IPOPT, showing that ignoring dry friction can cause actuator saturation and collisions, whereas friction-aware models yield safer trajectories with minimal final payload swing. The results support the practical relevance for industrial cranes and demonstrate robustness to friction parameter uncertainty up to about 100%.

Abstract

This paper presents an optimal trajectory generation method for 3D overhead cranes by leveraging differential flatness. This framework enables the direct inclusion of complex physical and dynamic constraints, such as nonlinear friction and collision avoidance for both payload and rope. Our approach allows for aggressive movements by constraining payload swing only at the final point. A comparative simulation study validates our approach, demonstrating that neglecting dry friction leads to actuator saturation and collisions. The results show that friction modeling is a fundamental requirement for fast and safe crane trajectories.

Figures (10)

• Figure 1: Schematic diagram of the overhead crane.
• Figure 2: Parameterization of the $i$-th obstacle model and visualization of the collision avoidance strategy.
• Figure 3: Example of the trajectory optimization process. The figure shows the initial guess, and the final optimized trajectories for the trolley and the payload.
• Figure 4: Planned (target) vs. simulated trajectories for Scenario 1. Each row corresponds to a model: Complete (top), Simplified (middle), and No Dry Friction (bottom)
• Figure 6: Planned vs. simulated trolley position and rope for NFM nominal performance analysis.