Control of planar parallel robots by applying distinct hybrid techniques in the task space

Abstract

During the last two decades, parallel robots have become more ubiquitous, employed in a great variety of sectors, from food to aerospace industries. In fact, they are much more efficient than their serial counterparts in terms of performing fast motions and consuming less energy. However, due to their mechanical complexity, they present a highly complex non-linear dynamics, which makes the modelling and control tasks difficult. Aiming to improve the performance and robustness of the control laws already used to control this type of mechanisms, previously, the authors proposed two novel laws of hybrid control, implemented in the joint space, in order to improve the dynamic behavior of parallel robots when performing fast motion tasks. Among the goals of the current work, one can mention to adapt the two laws of hybrid control, proposed in the previous work, by implementing them in the task space. Additionally, the peculiarities related to the dynamic formulation and the tuning of controller gains are also shown. Furthermore, a comparison of the performances of the pure and hybrid control techniques, implemented in both joint and task spaces, is presented as well, by executing the same paths and using adequate metrics. In the selected paths, experiments revealed that the hybridization process of pure control laws in the task space provides a significant reduction of the path-tracking and steady-state errors.

Appendix A. Experimental test bed

The dimensional parameters are the lengths $\ell _0$, $\ell _1$, $\ell _2$, $\ell _{j.1}$, $\ell _{j.2}$, while the inertial parameters are the masses $m_{\textrm{L}_{j.1}}$, $m_{\textrm{L}_{j.2}}$, and the mass moments of inertia $J_{\,\textrm{L}_{j.1}}$, $J_{\,\textrm{L}_{j.2}}$ with respect to the centre of mass of each moving link that belongs to the kinematic chain $\mathcal {K}_j$ (Fig. 3, Table 5). Additionally, $b_j$ and $\mu _j$ are, respectively, the viscous and dry friction coefficients at the actuated revolute joints.

Figure 15 shows the components of the robot systems. Constructively, the mechanical system (Fig. 16) has five revolute joints which correspond to rigid ball bearings. For the moving links, flat bars made of aluminum alloy and acrylic are employed. In addition, once the motion plane is horizontal, the dynamic model does not take into account the gravitational forces [44].

Regarding the actuation system, it is composed of two direct drive DC motors (250 W each) AMETEK PM70, one motor driver Pololu Dual VNH5019, and a switched-mode power supply (24 V, 390 W). The control system has two incremental rotary encoders E40S (5000 quad-counts per turn) and one microprocessor Raspberry Pi 2 model B. Additionally, there is an electronic circuit board for the conversions of the voltage levels, from the power supply to the encoder (24 to 15 V), and from the encoders to the microprocessor (0–15 to 0–3.3 V).