Adaptive Passivity-Based Pose Tracking Control of Cable-Driven Parallel Robots for Multiple Attitude Parameterizations

TL;DR

The paper tackles robust pose tracking for overconstrained cable-driven parallel robots (CDPRs) under uncertain dynamics and with flexible attitude representations. It introduces an adaptive feedforward-based controller coupled with an input-strictly passive (ISP) or strictly positive real (SPR) feedback law, designed to work with unconstrained attitude parameterizations, quaternions, or direction cosine matrices. The authors provide a rigorous passivity-based stability analysis and demonstrate asymptotic pose convergence across multiple parameterizations, supported by numerical simulations with rigid and flexible cables. This framework offers a flexible, robust approach to CDPR control that can adapt to different attitude representations without sacrificing stability guarantees, facilitating broader practical deployment.

Abstract

The proposed control method uses an adaptive feedforward-based controller to establish a passive input-output mapping for the CDPR that is used alongside a linear time-invariant strictly positive real feedback controller to guarantee robust closed-loop input-output stability and asymptotic pose trajectory tracking via the passivity theorem. A novelty of the proposed controller is its formulation for use with a range of payload attitude parameterizations, including any unconstrained attitude parameterization, the quaternion, or the direction cosine matrix (DCM). The performance and robustness of the proposed controller is demonstrated through numerical simulations of a CDPR with rigid and flexible cables. The results demonstrate the importance of carefully defining the CDPR's pose error, which is performed in multiplicative fashion when using the quaternion and DCM, and in a specific additive fashion when using unconstrained attitude parameters (e.g., an Euler-angle sequence).

Figures (8)

• Figure 1: A $6$ DOF CDPR with 8 flexible cables and a rigid-body payload.
• Figure 2: Block diagram of a CDPR with an adaptive feedforward-based control input and pretension & force distribution satisfying $\mbf{f} = {\boldsymbol{\Pi}}^{\mathsf{T}}({\boldsymbol{\rho}}){\boldsymbol{\tau}}$ which is proven to be passive in Theorem \ref{['theorem1']}. The passive system is in negative feedback with an ISP controller.
• Figure 3: Payload pose trajectory versus time with the $SO(3)$-based controller simulated with flexible cables: actual pose (solid) and desired pose (dashed). The payload attitude is expressed in terms of a 3-2-1 Euler-angle sequence only for visualization purposes.
• Figure 4: Winch torques versus time for the simulation with the $SO(3)$-based controller and flexible cables.
• Figure 5: Estimated parameters ${\hat{\mbf{a}}}$ versus time for the simulation with the $SO(3)$-based controller and flexible cables. The two subplots are the mass parameter (denoted $\hat{m}$) and inertial parameters (denoted $\hat{I}_{ij}$).

Theorems & Definitions (13)

• Definition 1: Passivity Brogliato2020
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 1
• proof
• Corollary 1