Energy-efficient control of a screw-drive pipe robot with consideration of actuator’s characteristics
- Peng Li^{1, 2}Email author,
- Shugen Ma^{3, 4},
- Congyi Lyu^{2},
- Xin Jiang^{1} and
- Yunhui Liu^{2}
Received: 20 April 2016
Accepted: 27 June 2016
Published: 11 July 2016
Abstract
Pipe robots can perform inspection tasks to alleviate the damage caused by the pipe problems. Usually, the pipe robots carry batteries or use a power cable draining power from a vehicle that has many equipments for exploration. Nevertheless, the energy is limited for the whole inspection task and cannot keep the inspection time too long. In this paper, we use the total input energy as the cost function and a more accurate DC motor model to generate an optimal energy-efficient velocity control for a screw-drive pipe robot to make use of the limited energy in field environment. We also propose a velocity selection strategy that includes the actual velocity capacity of the motor, according to the velocity ratio \(k_{\mathrm{v}}\), to keep the robot working in safe region and decrease the energy dissipation. This selection strategy considers three situations of the velocity ratio \(k_{\mathrm{v}}\) and has a wide range of application. Simulations are conducted to compare the proposed method with the sinusoidal control and loss minimization control (minimization of copper losses of the motor), and results are discussed in this paper.
Keywords
Background
With the advancement of the robotics and industrial technology, many pipe robots have been developed to explore the pipes that have cracks or defects to avoid serious accidents [1–4].
Up to now, there are more focus on the energy-efficient control of robots [5, 6]. Robots that perform pipe inspection task are often in the field environment, and the energy is a crucial limitation to the time of execution of a task. Most of the pipe robots are driven by DC motors. If the energy-efficient method is applied to the pipe inspection system, the energy dissipation will be decreased and the total time of performing a task will be increased. The energy dissipated through many ways, but only controlling the armature current and field current losses is feasible [7, 8]; further, many researchers conducted on the loss minimization control of the DC motor [9, 10]. They use the armature resistance loss and field resistance loss as the performance index to reduce the energy dissipation, and get the optimal control law, but in the view of the total input energy that is drawn from the power source is usually not optimal.
This paper proposes an energy-efficient solution for the control of a screw-type pipe robot by using an improved DC motor model and employing the total input energy as the performance index that reflect the whole system energy consumption. Straight pipe structure is the most common type; thus, this paper is limited to discuss the condition that the pipe robot is used in the straight horizontal pipe. Additionally, sinusoidal fashion control and the loss minimization control that only considers armature resistance are used as the comparison methods.
Methods
The screw-drive pipe robot
Typical screw-drive robot is usually composed of a rotator, elastic support arms, rollers and a motor for driving. The rollers have a constant incline angle with respect to the cross section of the pipe. When the motor turns, the whole body moves forward. If the motor turns reversely, the body moves backward. To propel a screw-drive-type robot, one motor is enough for straight pipe and elbow. However, for the T-shape pipe, extra navigation mechanism is needed.
Motion equation of the DC motor
Basic equations of the DC motor
Efficiency of the DC motor
Motion and force analysis of the robot
Energy-efficient control
- 1.
Cruise start/stop mode: Cruise start mode is used to start the motor and the robot at a specified speed; then, the motor and the robot keep this speed moving to find the potential defect of the pipe. When the detecting camera finds the suspicious defect, the robot will stop and detect that area carefully; thus, stopping the robot is called cruise stop mode.
- 2.
Location mode: Sometimes, a segment of pipe need not to be checked; thus, the robot just passes by. The operator only inputs the displacement \(S_{\mathrm{f}}\) within the time \(t_{\mathrm{f}}\); then, the optimal velocity profile is generated according to the value of \(k_{\mathrm{v}}\), which is a speed ratio defined in (38).
Cruise start/stop mode
Under this mode, the final velocity \({\omega _{\mathrm{f}}}\) and the corresponding time \({t_{\mathrm{f}}}\) are given, and the optimal velocity profile is generated by the control law. After the time \({t_{\mathrm{f}}}\), the actuator of the robot will keep the value of \({\omega _{\mathrm{f}}}\) moving forward, since keeping the velocity invariant will result in the minimization of the extra consumption of the total input electrical energy. On the contrary, under the cruise stop mode, the initial motor velocity \({\omega _0}\) and the time \({t_{\mathrm{f}}}\) are given.
Location mode
Velocity constrains
Results and discussion
Parameters of the robot and motor [13]
Parameter | Value | Parameter | Value |
---|---|---|---|
P | 20 W (rated) | D | 0.19 m |
\({K_{\mathrm{t}}}\) | 0.0170 N m/A | \(\alpha\) | 15° |
\({K_{\mathrm{e}}}\) | 0.0170 V s/rad | \({T_{\mathrm{load}}}\) | 0.3 N m |
\({R_{\mathrm{a}}}\) | 1.17 Ω | \({J_{\mathrm{eq}}}\) | \(4\times {10^{-5}}\,\mathrm{kg}\,\mathrm{m}^2\) |
\({R_{\mathrm{h}}}\) | 212.6 Ω | \(_{\mathrm{total}}\) | 111 |
\(30{\omega _{\mathrm{m,r}}}/\pi\) | 6000 rpm | \({c_{\mathrm{m}}}\) | \(2\times {10^{- 5}}\) N m s/rad |
Summary of total input energy
S _{f} (m) | t _{f} (s) | I: \(\int _0^{{t_{\mathrm{f}}}} {{V_{\mathrm{a}}}{i_{\mathrm{a}}}} \mathrm{d}t\) | II: \(\int _0^{{t_{\mathrm{f}}}} {{i_{\mathrm{a}}}^2{R_{\mathrm{a}}}} \mathrm{d}t\) | III: \(\int _0^{{t_{\mathrm{f}}}} {{V_{\mathrm{a}}}{i_{\mathrm{a}}}} \mathrm{d}t\) |
---|---|---|---|---|
0.3 m | 4 | 14.79 (14.02) | 14.37 | 15.65 |
1.2 m | 10 | 76.09 (71.46) | 75.28 | 85.53 |
2.0 m | 15 | 134.91 (126.50) | 132.83 | 155.18 |
Figure 8b | 3.10 | 3.31 | 14.12 | |
Figure 11a | 23.30 (19.70) | 21.65 | 23.91 | |
Figure 11b | 83.82 | N/A | 86.40 |
Conclusion
This paper considers a more accurate motor model and uses total input energy as the cost function to generate energy-efficient control laws for a pipe inspection robot. This pipe robot has two working modes: driving mode and detecting mode. Robot needs to keep a speed to move or move a distance to check the pipe; thus, we propose two types control: One is cruise start/stop control, and the other is location control. For the cruise mode and location mode, we have derived the optimal velocity and propose a velocity selection strategy according to the \(k_{\mathrm{v}}\). This velocity selection strategy can guarantee the motor work in safe region, which also means decreasing the total input energy consumption, and can treat all the combinations of the \(S_{\mathrm{f}}\) and \(t_{\mathrm{f}}\). Results show that this method indeed saves the energy dissipation with the commonly used method, and provide more accurate model compared with the loss minimization control.
Declarations
Authors' contributions
A energy-efficient control law is proposed for a pipe robot by considering the characteristics of motor. Optimal velocity profiles are derived from two sets of boundary conditions. A velocity selection strategy is generated by considering the capacity of motor. All authors read and approved the final manuscript.
Acknowledgements
The authors would like to thank Dr. Rongchuan Sun for his help in programming. The work is a part supported by Shenzhen Peacock Plan Team Grant (KQTD20140630150243062), Shenzhen Key Laboratory Grant (ZDSYS201405081618 25065), the Hong Kong Research Grants Council (CUHK6/CRF/13G) and the Hong Kong Innovation and Technology Fund (ITS/112/15F).
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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