Elsevier

ISA Transactions

Volume 84, January 2019, Pages 187-205
ISA Transactions

Practice article
An improved force-based impedance control method for the HDU of legged robots

https://doi.org/10.1016/j.isatra.2018.09.002Get rights and content

Highlights

  • Key reasons affecting the accuracy of the traditional force-based impedance control.

  • Dynamic compliance composition of both force inner loop and impedance outer loop.

  • Control accuracy of the traditional force-based impedance control is improved.

Abstract

Hydraulic drive mode enables legged robots to have excellent characteristics, such as greater power-to-weight ratios, higher load capacities, and faster response speeds than other robots. Nowadays, highly integrated valve-controlled cylinder, called hydraulic drive unit (HDU), is employed to drive the joints of these robots. However, various robot control issues exist. For example, during the walking process of legged robots, different obstacles are encountered, making it difficult to control such robots because the load characteristics of the ends of their feet change with the environment. Furthermore, although the adoption of HDU has resulted in high-performance robot control, the hydraulic systems of these robots still have problems, such as strong nonlinearity, and time-varying parameters. Consequently, robot control is very difficult and complex. This paper proposes an improved second-order dynamic compliance control system, impedance control, for HDU. The control system is designed to rectify the issues affecting the impedance control accuracy of the dynamic compliance serial–parallel composition between the HDU force control inner loop and the impedance control outer loop. Specifically, it consists of a compliance-enhanced controller and a feedforward compensation controller for the force control inner loop. Furthermore, the dynamic compliance composition of the inner and outer HDU control loops is rearranged. The results of experiments conducted indicate that the proposed method significantly improves the control accuracy compared to that of traditional force-based impedance control.

Introduction

Legged robots, compared with wheeled robots [1], tracked robots [2] and spherical robots [3], are better at adapting to unknown and unstructured environments. Currently, robot researchers from around the world are paying greater attention to this type of robot. Generally, every single leg of the legged robot has multiple active degrees of freedom. Every active degree of freedom consists of a valve-controlled cylinder, which is called a hydraulic drive unit (HDU) [4], [5], [6].

With the application of the HDU, high performance of the hydraulic system is shown in the robot. However, certain common problems of the hydraulic system cannot be ignored, such as strong nonlinear characteristic and time-varying parameters. However, the robot legs do work in difficult environments, such as snow or sand. These different working environments provide different load characteristics for the robot foot ends. This property makes the load characteristics, which act on the leg joints, complex and variable. Therefore, the robot control becomes more difficult. In terms of the control for the leg joints of a legged robot, the general control method is dynamic compliance control. By adopting this control method, the robot foot end can possess a certain dynamic compliance to effectively reduce the rigid impact when it contacts the load with greater stiffness, such as the ground. One of the most commonly applied dynamic compliance control methods is impedance control. The impedance control method can make the system equivalent to a second order mass–spring–damping system with a desired stiffness, damping and mass. Many researchers have conducted extensive research on the traditional impedance control method [7], [8], [9], [10], [11], [12], [13].

In recent years, this control method has been applied broadly in the domain of a motor driven robot, such as Tekken [14], Scout [15], KOLT [16], MIT cheetah robot [17], LittleDog [18], and humanoid Roboray [19]. With the development of hydraulic technology, the hydraulic driven legged robot is gradually becoming the hotspot for current research. The impedance control method is applied in this type of robot, such as Bigdog [20], HyQ [21], Scalf-1 [22], LWR robot [23], and StarlETH [24]. When conducting a dynamic compliance control on the HDU of a hydraulically driven robot, the basic principle can be described as follows. The HDU system is taken as the control inner loop, then the dynamic compliance control outer loop is applied in the control system. Therefore, the system can possess certain dynamic compliance by changing the input signal of the control inner loop through control outer loop. In terms of working conditions, robots usually operate in challenging and dynamically changing environments. Thus, precise kinematic planning for each type of contact is not a feasible solution. Under this situation, the force control system has better advantages over the position control system for its rapid response speed. Therefore, the paper focuses on the research of force-based impedance control.

Additionally, traditional position-based or force-based impedance control generally uses the inner loop system as the ideal system. The entire accuracy of dynamic compliance is not only determined by the impedance control of the outer loop but, but it is also greatly determined by the control accuracy of inner loop system. The high order dynamic compliance, which exists in the inner loop system, may affect the entire desired dynamic compliance of the robot. Particularly, when the desired dynamic compliance of robot is not precise, there will be negative influence on certain aspects of the robot, such as the buffering effect, gait, stability, and walking speed. Under the ideal situation, the inner loop of the force-based impedance control adopts a force closed loop. Due to the natural characteristic of the force closed loop, the dynamic compliance of the inner loop tends to be infinite. In other words, the force control has a rather high accuracy and the accuracy is not affected by the disturbance position. Thus, the control accuracy of the impedance outer loop is not affected by the control accuracy of the inner loop. However, under the actual working condition, a number of uncertain factors cannot be ignored. For example, the working environment or disturbance of the HDU force control system is uncertain. Those factors cause the disturbance and the load characteristic to affect the force control accuracy. Therefore, what dynamic compliance the force-based impedance control has in its inner and outer loop should be determined and analyzed. Based on this analysis, the compensation control should be applied to the inner loop dynamic compliance. In recent years, researchers around the world have gone to great lengths researching the high accuracy and robustness control aimed at the force control system, not limited to the hydraulic force control system [25], [26], [27], [28], [29]. According to the research results, not limited those cited in this paper, the performance analysis and optimization for control performance are conducted on the force control system. The control effect is good, but most of the control methods applied in these studies are advanced control algorithms, which have a certain complexity. Particularly, the dynamic compliance composition of the force control system is not proposed in the control methods mentioned above. Therefore, the targeted compensation for the force control has a slight deficiency.

In the authors’ former research, the mathematical models of both the position control system and the force control system for the first generation of HDU were built, and the sensitivity characteristics of the main parameters were analyzed, which provide references for the modeling of HDU in this paper [5], [30]. Moreover, the dynamic compliance composition was researched to improve the disturbance rejection ability of both the position control and force control systems [31], [32]. Based on the former works, two problems regarding the force-based impedance control are discussed in this paper.

First, in traditional impedance control systems, the inner loop is often considered to be ideal. In reality, the natural nonlinearity, time-variation and strong coupling of the hydraulic system make the inner loop non-ideal. The characteristics of the inner loop generate non-ideal inner loop dynamic compliance. Therefore, the control performance is not only influenced by the outer loop, but it is also greatly influenced by the accuracy of the inner loop. The influence of the non-ideal inner loop dynamic compliance on the impedance performance needs to be studied.

Second, after the key factors that influence the force-based impedance control are discovered, a compensation controller needs to be designed for the various factors to ensure the control performance in different working conditions.

The research on the origin of the above two problems is the main contribution in this paper, and the organization of this paper is listed as follows. First, the nonlinear mathematical model of the HDU force control system is introduced. Second, based on the basic principle of the traditional force-based impedance control, the implementation of this control method on the HDU is researched experimentally. Aimed at the experimental analysis, the control strategy for improving the traditional force-based impedance control is designed. Third, the dynamic compliance composition of the traditional force-based impedance control is researched. Thus, the serial–parallel composition of the dynamic compliances for the HDU inner loop and outer loop are obtained, which is one of the contribution in this paper. Moreover, the compliance-enhanced controller with multiple serial branches is proposed, which is targeted at each part of the dynamic compliance of the HDU force control inner loop. On the basis of this compliance-enhanced controller, another feedforward compensation controller for inner loop is designed to improve the dynamic compliance of the force control inner loop and the force control performance. Thus, the serial–parallel composition of the force-based impedance control dynamic compliance is rearranged to increase the control accuracy. This control method is the improved force-based impedance control, which is another contribution of our research. Finally, the validity of this control method is verified experimentally through the HDU performance test platform.

Section snippets

Introduction of HDU

The photos of the HDU, the single leg and the quadruped robot prototype are shown in Fig. 1. They are all situated in our laboratory or cooperative laboratory. The HDU is a servo valve-controlled symmetrical cylinder shown is Fig. 1(c). The HDU is the joint actuator of the leg hydraulic drive system shown in Fig. 1(b). The leg hydraulic drive system is a single leg of the legged robot prototype shown in Fig. 1(a).

The force closed loop control transfer block is shown in Fig. 2 [4], [30].

In Fig. 2

The traditional force-based impedance control

The impedance control is a typical control method of second order dynamic compliance. The dynamic compliance is defined as the ratio of system force error to the position error. In terms of position control system, the dynamic compliance is referred as the ratio of system disturbance force to output position. When this ratio is getting greater, it is indicated that the output position error is getting smaller under the effect of disturbance force. Thus, the dynamic compliance is getting

Control strategy

According to Section 3.3, the HDU adopting the traditional force-based impedance control does not possess the desired compliance. Therefore, the difference between the actual control effect and the desired control effect cannot be ignored. This difference tends to be more obvious when the disturbance position signal has a greater amplitude or a higher frequency. Therefore, the requirement of a high accuracy control performance for the legged robot cannot be achieved in this situation. In other

Experiment principle

Combined the compliance-enhanced compound controller Gcf(s) designed in Section 4.3 and the feedforward compensation controller Gff(s) designed in Section 4.4, the experiment principle of HDU performance test platform is shown in Fig. 24.

The control effect

In order to prove the control effect of the compensation controllers Gcf(s) and Gff(s), the experiment plan same as the Table 2 in Section 3.3 is conducted in this section. In order to present the control effect of different controllers in a better way, the

Conclusion

The dynamic compliance of the force-based impedance control inner loop is not infinite. This dynamic compliance contains two parts. The first part is defined as the natural dynamic compliance Zsf1. The second part is defined as the equivalent dynamic compliance Zsf2. These two dynamic compliances work together and have a serial relationship during the system inner loop control process, which also varies as the load working conditions change. Moreover, the inner and outer loop dynamic

Acknowledgments

The project is supported by National Natural Science Foundation of China (51605417), National Key Basic Research Program of China (973 Program, No. 2014CB046405) and Ph. D. Programs Foundation of Yanshan University (BL18027).

Xiang-dong Kong, born in 1959, is currently a professor at Yanshan University, China. He serves as the chairman of Fluid Transmission and Control Society which is a branch of Chinese Mechanical Engineering Society (CMES). His main research interests include electro-hydraulic servo control system, heavy machinery fluid transmission and control and robot design and control.

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    Xiang-dong Kong, born in 1959, is currently a professor at Yanshan University, China. He serves as the chairman of Fluid Transmission and Control Society which is a branch of Chinese Mechanical Engineering Society (CMES). His main research interests include electro-hydraulic servo control system, heavy machinery fluid transmission and control and robot design and control.

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