Model-Based Control of a 4-DOF Rehabilitation Parallel Robot with Online Identification of the Gravitational Term

Abstract

Parallel robots are being increasingly used as a fundamental component of lower-limb rehabilitation systems. During rehabilitation therapies, the parallel robot must interact with the patient, which raises several challenges to the control system: (1) The weight supported by the robot can vary from patient to patient, and even for the same patient, making standard model-based controllers unsuitable for those tasks since they rely on constant dynamic models and parameters. (2) The identification techniques usually consider the estimation of all dynamic parameters, bringing about challenges concerning robustness and complexity. This paper proposes the design and experimental validation of a model-based controller comprising a proportional-derivative controller with gravity compensation applied to a 4-DOF parallel robot for knee rehabilitation, where the gravitational forces are expressed in terms of relevant dynamic parameters. The identification of such parameters is possible by means of least squares methods. The proposed controller has been experimentally validated, holding the error stable following significant payload changes in terms of the weight of the patient's leg. This novel controller allows us to perform both identification and control simultaneously and is easy to tune. Moreover, its parameters have an intuitive interpretation, contrary to a conventional adaptive controller. The performance of a conventional adaptive controller and the proposed one are compared experimentally.

Keywords: adaptive control; dynamic parameter identification; parallel robot; relevant parameters.

Figure 1

Movements required for knee rehabilitation.

Figure 4

Friction experiments for (a) compression and (b) traction.

Figure 2

Architecture of the 4-DOF PR.

Figure 3

Decomposition of general forces in a rehabilitation trajectory (a) $\overrightarrow{G}$, $\overrightarrow{F_f}$; (b) ${\overrightarrow{F}}_{in}$, ${\overrightarrow{F}}_{cyc}$.

Figure 5

Friction responses and models for (a) the external limbs and (b) the central limb of the 3UPS+RPU PR.

Figure 6

Base parameters with 95% dynamic influence.

Figure 7

Window-based control scheme with online relevant parameter identifier.

Figure 8

Actual robot and illustration of the stages of the experiment.

Figure 9

Trajectory tracking of $q_{23}$ and comparison with the PD+G controller.

Figure 10

Control actions of the raw PDG, RLS, and adaptive controllers for the second actuator.

Figure 11

WLS (a) and RLS (b) estimation of the first relevant parameter. Comparison with the adaptive controller.

Figure 12

Estimation of the first (a) and second (b) relevant parameters, and error (c) of the second joint with the RLS controller.