In this paper, an energy-efficient control solution for an Unmanned Ground Vehicle (UGV) in a Wireless Sensor Network is proposed. This novel control approach integrates periodic event-triggered control, packet-based control, time-varying dual-rate Kalman filter-based prediction techniques, and dual-rate control. The systematic combination of these control techniques allows the UGV to track the desired path preserving performance properties, despite (i) existing scarce data due to the reduced usage of the wireless sensor device, which results in less number of transmissions through the network and, hence, bandwidth and battery saving; (ii) appearance of some wireless communication problems such as time-varying delays, packet dropouts, and packet disorder; and (iii) coping with a realistic scenario where external disturbance and sensor noise can arise. The main benefits of the control solution are illustrated via simulation.
A Wireless Sensor Network (WSN) [
Differently from traditional networks, a WSN has its own design and resource constraints. Resource constraints include short communication range, a limited amount of energy (which is supplied by battery), low bandwidth, and limited processing and storage capabilities (being not capable of running complex control algorithms). As sensor nodes operate on limited battery power, and data transmission is very expensive in terms of energy consumption [
In periodic event-triggered control (PETC) [
Regarding event-based state prediction techniques, different approaches address this aspect in the literature, for instance, distributed event-triggered filtering in [
Packet-based control [
In dual-rate control [
In order to show the potential of the ideas posed in this work, the control solution is employed in the context of a popular control application, that of Unmanned Ground Vehicles (UGVs). In fact, the large number of UGV applications such as target tracking, inspection, and mapping has attracted the attention of the scientific community (see, e.g., [
In summary, the main contribution of the present work is the development of a novel and complete approach for WSNs, where a TVDRKF, a dual-rate controller, and a Pure Pursuit path tracking algorithm are systematically brought together in a PETC scenario in order to considerably lessen resource usage (energy and bandwidth), and dealing with some wireless communication problems and disturbance and noise, while keeping satisfactory control properties.
Finally, the work is structured as follows. Section
The energy-efficient control solution taken into account in this work is illustrated in Figure
An energy-efficient control system for a WSN.
As said in the previous section, dual-rate control is used in the proposed approach. Then, two different periods are considered:
To avoid packet disorder, in this work, it is strictly necessary to know the maximum round-trip time delay
As is well-known, if UDP is used as the transport layer protocol, packet dropouts may appear. Since this phenomenon is basically random [
Next, the two components (sensor node and base station) and the signals involved in the energy-efficient control system are detailed.
As shown in Figure
The base station includes the control algorithm, which integrates a time-varying dual-rate Kalman filter (TVDRKF), a Pure Pursuit path tracking algorithm (which receives the desired path from the reference generator), and a dual-rate controller. In addition, an event-triggered condition is defined in order to decide when the control signal is sent to the actuator located at the sensor node. This condition is assessed only when a sampled output is received from the sensor. Thus, unlike the condition included at the sensor, the condition defined at the base station is not periodically evaluated.
Next, the proposed scenario is described (more details can be found in Section When the periodic event-triggered condition is satisfied at the sensor, a new output From From From From From When the event-triggered condition at the base station is satisfied, the current control signal
Next, each component of the control system is defined in detail.
Considering state-space representation, the model of the plant at sampling period
In addition,
Using
Given a broadband noise
Assuming the following notation:
Let us denote
When
Observe that the feedback loop is only closed from sensor node to base station and back to sensor node, when the conditions (
Considering
Taking into account (
Due to the nonuniform nature of the pattern,
From the notation
Structure of the time-varying dual-rate Kalman filter.
From the desired kinematic reference
The path tracking algorithm generates the dynamic reference based on the rotational velocity for both wheels, i.e.,
While direct kinematics specifies the positions that the UGV is able to reach by giving the wheel speed, differential kinematics establishes relations between motion (velocity) in joint space and motion (linear/angular velocity) in task space (e.g., Cartesian space). A two-wheel UGV rotates with respect to a point located in some place of the axis, which is shared by the two wheels. This point is known as Instantaneous Rotation Center (IRC), that is, the point with zero velocity at a particular instant of time in a body undergoing planar movement. IRC varies according to wheel speed variations.
Each wheel follows a trajectory with the same rotational velocity
The Pure Pursuit algorithm is based on the computation of the curvature
Circumference between the current point and the target point.
As can be seen, the control law
For a desired linear velocity
The path tracking algorithm requires determining one point located at a minimum distance from the current point, i.e., the so-called Look Ahead Distance (LAD), not considering the nearest points in the prescribed trajectory. This procedure avoids a severe correction, and hence, it leads to a soft movement.
Finally, these are the steps to be followed when the main loop of the Pure Pursuit algorithm is implemented (depicted in more detail in Figure UGV rotational and linear velocity calculation from system output estimations and corrections provided by the TVDRKF at period UGV position and orientation computation in the time period Generation of the future reference for the robot, Control law computation: from
Structure of the Pure Pursuit path tracking algorithm.
In this work, in order to reach the desired control performance, a dual-rate controller is used. From
Different alternatives can be followed to design a dual-rate controller (see, e.g., in [ a slow-rate subcontroller a digital hold a fast-rate subcontroller
where the input of
Structure of the dual-rate controller.
In this section, certain cost indexes closely related to control performance and resource usage will be presented. By means of these indexes, the energy-efficient control proposal may be compared with the conventional time-triggered control strategy. Regarding control performance, similar to [
To analyze the reduction of the resource usage in the energy-efficient control solution compared to the traditional time-triggered control, the cost index
In this section, the main advantages of the energy-efficient control solution compared to the time-triggered one will be shown. The study will be focused on the trade-off between resource usage and control properties. The section is split into two parts. Firstly, important data used for the simulation will be presented (transfer function, delay distribution, control parameters, and so on). Secondly, the cost indexes introduced in Section 4 will be evaluated by means of a TrueTime application [
Considering a similar model for both wheel motors, the model is described by means of this transfer function:
From previous off-line experiences on this WSN framework [
In this simulation, let us assume the packet dropout probability as
The discrete-time controller design comes from the discretization at different periods of this continuous-time PID controller, which is designed following classical procedures [
The dual-rate controller is obtained by means of (
The disturbance, which is defined at period
The time-varying dual-rate Kalman filter (TVDRKF) is designed considering the augmented state resulting from the consequent state-space realization (
The positive constants in (
Finally, the reference to be followed includes a sequence of four right angles.
Starting from a time-triggered single-rate control scenario with neither noise nor disturbance and neither time-varying delays nor packet dropouts and using the controller at period
Time-triggered single-rate control at period
Time-triggered single-rate control at period
Time-triggered dual-rate control (no noise, no disturbance, no delays, and no dropouts).
Dual-rate time-triggered control (no noise and no disturbance but with delays and dropouts).
If the TVDRKF is incorporated into the time-triggered dual-rate control system, where packet-based control is also integrated, the performance is clearly improved (illustrated in Figure
Time-triggered dual-rate control, with TVDRKF, and packet-based control (noise, disturbance, delays, and dropouts).
Disturbance estimation by TVDRKF.
Finally, event-triggered conditions are added to the WSN, and then, the system becomes a periodic event-triggered dual-rate control system. The performance obtained is similar to that reached by the time-triggered version of the system (see in Figure
Periodic event-triggered dual-rate control, with TVDRKF, and packet-based control (noise, disturbance, delays, and dropouts).
To analyze the previous conclusions in more detail, the cost indexes presented in Section 4 are calculated for each scenario. Table a: time-triggered single-rate control scenario at period b: time-triggered single-rate control scenario at period c: time-triggered dual-rate control scenario d: time-triggered dual-rate control scenario, adding TVDRKF, and packet-based control e: periodic event-triggered dual-rate control scenario, with TVDRKF, and packet-based control
Cost indexes.
Index | a | b | c | d | e |
---|---|---|---|---|---|
1671.8 | 1043.4 | 1029.9 | 1030.0 | 1184.4 | |
44.55 | 38.76 | 44.33 | 44.33 | 44.97 | |
22.4 s | 22.0 s | 22.0 s | 22.0 s | 22.0 s | |
50% | 100% | 50% | 48.18% | 26.13% |
As previously commented, the desired, nominal performance is presented by scenario b, and hence,
As a summary, the proposed control approach is able to significantly reduce resource usage (around 75%) while keeping satisfactory control properties, which is only worsened by around 15% on average, and despite the existence of wireless communication problems such as time-varying delays and packet dropouts.
The proposed energy-efficient control solution for a UGV in a WSN enables lessening the amount of transmissions through the network, which results in bandwidth and battery saving, despite keeping a satisfactory system performance. The solution integrates dual-rate control, periodic event-triggered control, packet-based control, and time-varying dual-rate Kalman filter-based prediction techniques. Additionally, the approach deals with wireless communication problems (such as time-varying delays, packet dropouts, and packet disorder) and copes with a realistic scenario, where measurement noise and external disturbance can occur.
The data can be provided under petition.
The authors declare that they have no conflicts of interest.
This research work has been developed as a result of a mobility stay funded by the Spain Visiting Fulbright Scholar Programme of the Fulbright Commission and the Spanish Ministry of Education under “Programa Estatal de Promoción del Talento y su Empleabilidad en I+D+i, Subprograma Estatal de Movilidad, del Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016.” In addition, the research was funded in part by Grant RTI2018-096590B-I00 from the Spanish Government and by the European Commission as part of Project H2020-SEC-2016-2017—topic: SEC-20-BES-2016—ID: 740736—“C2 Advanced Multi-domain Environment and Live Observation Technologies” (CAMELOT). Part WP5 supported by Tekever ASDS, Thales Research and Technology, Viasat Antenna Systems, Universitat Politècnica de València, Fundação da Faculdade de Ciências da Universidade de Lisboa, Ministério da Defensa Nacional-Marinha Portuguesa, Ministério da Administração Interna Guarda Nacional Republicana.