Modelling and analysis of quadruped walking robot using singular system theory

In this paper, the discrete- and continuous time dynamic input-output control models, the consumption-tracking models, are considered. Generally, these models are described by the linear-quadratic singular systems. So this paper, by using the singular system theory, investigates the optimal regulation problems of these models. The optimal controls of both discrete- and continuous-time linear-quadratic singular systems we derived.

In this paper, in order to meet the requirements of stable foot support and balanced walking of quadruped hydraulic robot, a new control method is proposed. The "hard" contact between the feet of the quadruped hydraulic robot and the ground are changed into "semi flexible" contact to reduce the impact force produced by the contact and collision of the two and reduce the unbalance of the force. The designed "semi flexible" scheme was to coat the "semi flexible" modified polytetrafluoroethylene (PTFE) material on the surface of the bottom material of the robot's foot. The modification of PTFE was optimized by SRIM, and the optimization scheme was selected for experimental study to obtain the Al2O3/PTFE material for which the abrasive resistance met the requirement of robot motion. It was also used in robot force imbalance control experiment research optimization. The study clearly revealed that it can effectively reduce the power of the impact force caused by the contact and collision of the feet of the quadruped robot and the ground, reduce the swing and the unbalance of the motion force of the quadruped robot, and meet the requirements of the precise positioning and the force balance walking of the motion of quadruped hydraulic robot to a certain extent.

The stabilization problem of singular linear large-scale control systems with input feedbacks is investigated by using Riccati matrix equation, generalized Lyapunov function method, system decomposition method, singular systems theory and matrix theory. Some sufficient conditions for determining the asymptotical stability and unstability of the corresponding singular closed-loop large-scale systems are given. At last, an illustrate example is given to show the application of main result.

Over the last decades there has been substantial progress on the development of theory and numerical methods for singular systems (known also as descriptor systems, semistate systems, differential alge-braic systems, generalized state-space systems, etc.). The need for such methodsarisen primarily from the increased practical interest for a more general system description which takes the intrinsic physical sys-tem model structure into account. Besides that, many physical process-es are most naturally and easily modelled as mixed systems of differen-tial and algebraic equations (DAE). As the title implies the paper de-scribes the singular systems theory application in power systems dy-namics simulation, particularly considered an alternative method for energy systems’ mathematical models formulation based on the singu-lar systems theory elements with some indicative examples illustrating feasibility and efficiency of this approach

This paper deals with the exponential stabilization problem by means of memory state feedback controller for linear singular positive systems with delay. By using system decomposition approach, singular systems theory and Lyapunov function method, we obtain new delay-dependent sufficient conditions for designing such controllers. The conditions are given in terms of standard linear programming (LP) problems, which can be solved by LP optimal toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.

A singular biological economic model with harvesting and stage structure is presented. The local stability of equilibriums of the system is investigated when the economic profit parameter is zero, and the conditions of the singularity induced bifurcation occurring at the positive equilibrium are obtained by the singular systems theory and bifurcation theory. In order to eliminate the singularity induced bifurcation, a state feedback controller is designed by controlling the fishing effort. At last, an application example is given to illustrate the validity of the theoretical results.

We analyzed some singular distributed parameter system(SDPS) with boundary conditions in high dimension bounded domain with sufficiently smooth boundary. With the spectrum theory in PDE, the systems initially is formulated as an infinite-dimensional singular systems. The state space representation of the system is built according to matrices decomposition method. And the admissible property is discussed. By the singular system theory some novel uniform state feedback controller is designed.

For an easier and natural teleoperation of the quadruped walking robots, a user interface is developed with a steering wheel and an assembly of pedals. In order to change the speed and the direction of the quadruped walking robots according to the operation of the steering wheel and the pedal, an online gait transition method is developed. Using this human-machine interface and online gait transition, the operator can control the quadruped walking robots almost in the same way as a driver drives a car. A quadruped walking robot named JROB-2 is used in the experiments. As the steering wheel is also equipped with various control buttons, it is possible to assign various single command tasks, like stand up and sit down etc., to these buttons and hence control the robot for these tasks without even touching the keyboard or mouse. The paper presents the details of this interface.

This paper proposes a quadruped walking robot that has high performance as a working machine. This robot is needed for various tasks controlled by tele-operation, especially for humanitarian mine detection and removal. Since there are numerous personnel landmines that are still in place from many wars, it is desirable to provide a safe and inexpensive tool that civilians can use to remove those mines. The authors have been working on the concept of the humanitarian demining robot systems for 4 years and have performed basic experiments with the first prototype VK-I using the modified quadruped walking robot, TITAN-VIII. After those experiments, it was possible to refine some concepts and now the new robot has a tool (end-effector) changing system on its back, so that by utilizing the legs as manipulation arms and connecting various tools to the foot, it can perform mine detection and removal tasks. Toaccomplish these tasks, we developed various end-effectors that can be attached to the working leg. In this paper we will discuss the mechanical design of the new walking robot called TITAN-IX to be applied to the new system VK-II.

Reduction of the energy consumption is one of the most important problems to utilize quadruped walking robots for various works on rugged terrain. The authors have studied basic strategy to achieve high energy efficiency when the quadruped walking robot do the motion essentially requires positive power by the analysis of body rising motion. This paper discusses the energy efficiency of the slope walking motion by the quadruped walking robot. First, we investigate the walking posture in consideration of ideal actuator characteristics where the robot consumes few negative powers at each joint which causes the main energy loss of the walking robot. Then, we investigate optimal walking posture in consideration of DC motor characteristics by the full search of three gait parameters which define the crawl gait. Furthermore, we derive the optimal walking motion by the optimization of three gait parameters which are kept constant during one cycle gait and instantaneous parameters such as body velocity and supporting forces changed at each moment simultaneously.

This paper investigates dynamic gait planning optimization and balance control of quadruped robots under external disturbance forces. First, a platform of quadruped walking robot with fourteen active degrees of freedom is designed. Then, a forward kinematic model of joints is built for quadruped robots based on Denavit-Hartenberg(D-H) method. The inverse kinematic equations are solved to result in joint values when the desired position and orientation are specified. A dynamic gait planning algorithm is proposed and tested on the quadruped robot. The planning function is established to create some point-to-point trajectories. The angle values of the joints can be calculated by using the inverse kinematics equations for every moment. Considering the external distribution a balance control approach is proposed to stabilize the robot based on the information from the attitude sensors. The walking is stabilized by a feedback control that uses a three-axis acceleration sensor. Experiments have been performed on the quadruped robot. The results showed that the proposed methods work well in dynamic gait planning and external disturbances of a quadruped bionic robot.

We have proposed the sway compensation trajectory of robot body to realize dynamically stable walking for a quadruped walking robot. This method uses the lateral motion of the robot body to keep a zero momentum point (ZMP) on a diagonal line between the support legs. However, energy consumption of the sway compensation trajectory is larger than the case without trajectory control because periodical acceleration of the body has to be generated to realize sway motion. In this paper, we propose a new sway compensation trajectory for a quadruped walking robot named 3D sway compensation trajectory. This method is the extension of conventional sway compensation trajectory toward three dimensional motion, and the position of ZMP is controlled not only by lateral body motion but also by longitudinal and vertical body motion. Next, we demonstrate that energy consumption for walking can be reduced by combining these motions through theoretical analysis and computer simulation, and an optimum 3D sway compensation trajectory that minimizes energy consumption is proposed. Optimum trajectory is applied to a quadruped walking robot and the validity of the proposed trajectory is verified using the dynamic motion simulator, ADAMS.

A new method, inspired by the gait of horses, for regulating the ground reaction force of a quadruped walking robot, is proposed. The method uses the mechanical stiffness switch with a dual‐spring structure inspired by an equine distal forelimb. This includes the use of a low‐stiffness spring activated at the moment of touchdown and a high‐stiffness spring for the support phase. This method has been applied to Jinpoong, a hydraulic quadruped walking robot, and has contributed to the robot's stable gait on uneven terrain.

Biological observations on tetrapods locomotion deduce that anti-phase synchronization (APS) between fore and rear parts is beneficial for achieving a high-speed walking. On the other hand, theoretical analysis and experimental studies on quadruped robots suggest that a flexible spine potentially improves the gait efficiency and adaptability via smoothing the ground collisions. However, these two mechanisms have never been placed together by a comprehensive investigation in terms of their synergetic effect. Namely, an advanced principle is still lacking in combining the APS and the spine flexibility for quadruped walking robots. To address this issue, we construct a mathematical model for a quadruped dynamic walker under different spine conditions. First, the APS effect is generated via entrainment-based control method under a rigid spine condition. Then, flexible spines realized by three kinds of springs are compared with the rigid one via theoretical analysis. The results suggest that the APS mechanism and the flexible spine can be synergized via an appropriate deformation control. The theoretical findings not only uncover locomotion control mechanisms for quadruped walking robots, but also provide additional understandings of tetrapods dynamic walking from a mechanical engineering point of view.

Quadruped robots have great agility, flexibility and stability, which enables them to walk through uneven terrain. Motion control of legged robots is always a difficult problem. Previous approaches mostly either use a predefined gait that results in clumsy and unnatural behavior, or use reinforcement learning approach to generate a gait strategy that needs longtime computation and elegant network design. In this paper, we present an effective approach that uses deep reinforcement learning with prior knowledge to optimize the gait of quadruped robot. By using a specific quadruped robot walking gait as a priori knowledge, this approach adopts the technique of distributed proximal policy optimization to optimize the search for better gait. The proposed approach does not require modelling of complex robots, and has good network convergence speed and learning effect. Simulation results demonstrate that our proposed approach converges faster than other deep reinforcement learning methods without prior knowledge. Besides, our achieved gait has higher speed that is 50% faster than the trot gait without optimization.