Assessment of an Average Tracking Controller that Considers all the Subsystems Involved in a WMR: Implementation via PWM or Sigma-Delta Modulation

Abstract

This paper has two aims; the first, to present the design of a three-level average controller (that do not require electromechanical sensors) for the trajectory tracking task in a differential drive wheeled mobile robot (WMR). Such a controller considers, for the first time in literature, the dynamics of the three subsystems composing a WMR, i.e., mechanical structure, actuators, and power stage. The proposed controller is designed as follows: At the high level, a kinematic control for the mechanical structure is proposed. At the medium level, a control based on differential flatness for the actuators is presented. And at the low level, an average flatness control for the power is proposed. The second aim of this paper is to present an assessment, via numerical simulations using MATLAB-Simulink, of the three-level average controller performance when it is implemented using a PWM or a Σ-Δ-modulator. In these simulations the robustness of the controller is shown when multiple abrupt variations are considered in some parameters of the WMR.

Tracking Control for Mobile Robots Considering the Dynamics of All Their Subsystems: Experimental Implementation

“…After carrying out the review of the literature associated with design of controllers for the trajectory tracking task in differential drive WMRs, it was found that, generally, this task has been solved in three directions: (a) by only using the kinematic or dynamic model of the mechanical structure , (b) by employing the kinematic/dynamic model of the mechanical structure along with the dynamics of the actuators [85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103], and (c) by considering the kinematic model of the mechanical structure along with the dynamics of the actuators and power stage [104,105]. In the last direction, contributions that have carried out interesting efforts are [106][107][108][109][110][111][112][113][114].…”

“…Motivated by the aforementioned ideas, the hierarchical control approach in mobile robotics (see [86,104,105,115]), and use of DC/DC converter-DC motor systems (see [116,117]), the purpose of the present paper is threefold. First, it aims, to introduce a three-level hierarchical controller that considers dynamics of the three subsystems that compose a WMR to solve, in a more complete way, the trajectory tracking task.…”

“…In [105], Sánchez et al proposed a kinematic controller for the WMR, a controller based on differential flatness for the actuators, and a differential flatness-based controller for the power stage. Controllers reported in [104,105] were tested only via numerical simulations.…”

“…In this subsection, controllers designed in Sections 4.1, 4.2, and 4.3 are integrated using a hierarchical approach (see [86,104,105,[115][116][117]) to solve the trajectory tracking task for a differential drive WMR when dynamics associated with each one of subsystems composing the WMR are considered (see Figure 1). Using the kinematic models associated with a differential drive WMR (1) and a reference robot (3), it was found that Complexity 7 velocity profiles and , ensuring ( , , ) → ( * , * , * ), are given by (8) and (9), respectively.…”

Robust Tracking Controller for a DC/DC Buck-Boost Converter–Inverter–DC Motor System

“…According to literature, several applications have benefited using DC/DC power electronic converters as drivers for DC motors [1][2][3][4][5][6][7]. Particularly, mechanical systems [1], robots [2][3][4], electric vehicles [5], and renewable energy [6,7]. Thereby, the design of controls for DC motors driven by DC/DC power converters is a current research topic.…”