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This paper aims to deal with the trade-off of the stability and the accuracy in learning human control strategy from demonstrations. With the stability conditions and the estimated stability region, this paper aims to conveniently get rid of the unstable controller or controller with relatively small stability region. With this evaluation, the learning human strategy controller becomes much more robust to perturbations.

In this paper, the criterion to verify the stability and a method to estimate the domain of attraction are provided for the learning controllers trained with support vector machines (SVMs). Conditions are formulated based on the discrete-time system Lyapunov theory to ensure that a closed-form of the learning control system is strongly stable under perturbations (SSUP). Then a Chebychev point based approach is proposed to estimate its domain of attraction.

Some of such learning controllers have been implemented in the vertical balance control of a dynamically stable, statically unstable wheel mobile robot.

The purpose of this paper is to present a two‐wheeled inverted pendulum with self‐tilt‐up motion ability. With this ability, the two‐wheeled inverted pendulum can erect without assistance, and then the vehicle can be autonomously deployed. The paper proposes an approach to achieve this self‐tilt‐up motion, which involves precessional motion.

A flywheel is mounted inside the vehicle to perform high‐speed spinning. The flywheel and body of the vehicle are forced to move around a fixed point and precessional motion occurs. As a result of the precessional motion, a moment is synchronously generated to tilt the body up to the upright position. Since no external force is applied on this two‐wheeled inverted pendulum, it is called self‐tilt‐up motion. A 3D model and a prototype are built to validate this approach.

The simulation and experimental results show that the self‐tilting‐up motion is successful.

This paper presents a self‐tilt‐up motion for a two‐wheeled inverted pendulum. With the analysis of the dynamics, simulation demonstrations and prototype development, the results show that the vehicle could perform self‐tilt‐up motion without any assistance. The principle of this self‐tilt‐up motion involves processional motion of rigid body. We also pointed out the factors that play important roles in influencing the performance of self‐tilt‐up motion and then define the switching time for the motion to switch to dynamic balance movement.

Traditional multi‐wheel robots cannot work when they overturn. However, the two‐wheeled inverted pendulums with self‐tilt‐up ability do not have this shortcoming. They can stand up to keep working even if they fall down. A two‐wheeled inverted pendulum with self‐tilt‐up ability can be applied to many places. Equipped with solar battery, it can be used as an independent explorer. This type of vehicle can be deployed in swarms for planetary detection. For example, many small two‐wheeled inverted pendulums assist a lunar rover for exploration, samples gathering, etc.

This paper aims to keep the pendulum on the linear moving car vertically balanced and to bring the car to the equilibrium position with the designed controllers.

As inverted pendulum systems are structurally unstable and nonlinear dynamic systems, they are important mechanisms used in engineering and technological developments to apply control techniques on these systems and to develop control algorithms, thus ensuring that the controllers designed for real-time balancing of these systems have certain performance criteria and the selection of each controller method according to performance criteria in the presence of destructive effects is very helpful in getting information about applying the methods to other systems.

As a result, the designed controllers are implemented on a real-time and real system, and the performance results of the system are obtained graphically, compared and analyzed.

In this study, motion equations of a linear inverted pendulum system are obtained, and classical and artificial intelligence adaptive control algorithms are designed and implemented for real-time control. Classic proportional-integral-derivative (PID) controller, fuzzy logic controller and PID-type Fuzzy adaptive controller methods are used to control the system. Self-tuning PID-type fuzzy adaptive controller was used first in the literature search and success results have been obtained. In this regard, the authors have the idea that this work is an innovative aspect of real-time with self-tuning PID-type fuzzy adaptive controller.

Intelligent control for unidentified systems with unstable equilibriums is not always a proper control strategy, which results in inferior performance in many cases. Because of the existing trial and error manner of the procedure in former duration of learning, this exploration for finding the appropriate control signals can lead to instability. However, the recent proposed emotional controllers are capable of learning swiftly; the use of these controllers is not an efficient solution for the mentioned instability problems. Therefore, a solution is needed to evade the instability in preliminary phase of learning. The purpose of this paper is to propose a novel approach for controlling unstable systems or systems with unstable equilibrium by model free controllers.

An existing controller (model‐based controller) with limited performance is used as a mentor for the emotional learning controller in the first step. This learning phase prepares the controller to control the plant as well as mentor, while it prevents any instability. When the emotional controller can imitate the behavior of model based one properly, the employed controller is gently switched from model based one to an emotional controller using a fuzzy inference system (FIS). Also, the emotional stress is softly switched from the mentor‐imitator output difference to the combination of the objectives. In this paper, the emotional stresses are generated once by using a nonlinear combination of objectives and once by employing different stresses to a FIS which attentionally modulated the stresses, and makes a subset of these objectives salient regarding the contemporary situation.

The proposed model free controller is employed to control an inverted pendulum system and an oscillator with unstable equilibrium. It is noticeable that the proposed controller is a model free one, and does not use any knowledge about the plant. The experimental results on two benchmarks show the superiority of proposed imitative and emotional controller with fuzzy stress generation mechanism in comparison with model based originally supplied controllers and emotional controller with nonlinear stress generation unit – in control of pendulum system – in all operating conditions.

There are two test beds for evaluating the proposed model free controller performance which are discussed in this paper: a laboratorial inverted pendulum system, which is a well‐known system with unstable equilibrium, and Chua's circuit, which is an oscillator with two stable and one unstable equilibrium point. The results show that the proposed controller with the mentioned strategy can control the systems with satisfactory performance.

In this paper, a novel approach for controlling unstable systems or systems with unstable equilibrium by model free controllers is proposed. This approach is based on imitative learning in preliminary phase of learning and soft switching to an interactive emotional learning. Moreover, FISs are used to model the linguistic knowledge of the ascendancy and situated importance of the objectives. These FISs are used to attentionally modulate the stress signals for the emotional controller. The results of proposed strategy on two benchmarks reveal the efficacy of this strategy of model free control.

Walking on inclined ground is an important ability for humanoid robots. In general, conventional strategies for walking on slopes lack technical analysis in, first, the waist posture with respect to actual robot and, second, the landing impact, which weakens the walking stability. The purpose of this paper is to propose a generic method for walking pattern generation considering these issues with the aim of enabling humanoid robot to walk dynamically on a slope.

First, a virtual ground method (VGM) is proposed to give a continuous and intuitive zero-moment point (ZMP) on slopes. Then, the dynamic motion equations are derived based on 2D and 3D models, respectively, by using VGM. Furthermore, the waist posture with respect to the actual robot is analyzed. Finally, a reformative linear inverted pendulum (LIP) named the asymmetric linear inverted pendulum (ALIP) is proposed to achieve stable and dynamical walking in any direction on a slope with lower landing impact.

Simulations and experiments are carried out using the DRC-XT humanoid robot platform with the aim of verifying the validity and feasibility of these new methods. ALIP with consideration of waist posture is practical in extending the ability of walking on slopes for humanoid robots.

A generic method called ALIP for humanoid robots walking on slopes is proposed. ALIP is based on LIP and several changes, including model analysis, motion equations and ZMP functions, are discussed.

This paper aims to examine the structure of the control strategy that is being deployed on the control of the mobile materials handling platform, from the higher level onboard interface software to the low‐level control system that is tasked with the dynamic stability of the platform.

The application of the principle of the inverted pendulum in mobile robotics has only recently been made possible by advances in the technology of electronics. A mobile materials handling platform has been designed and built for use in manufacturing systems of the future. The principle of the inverted pendulum has been incorporated into the design. This means that the platform is able to maintain dynamic stability during specific periods of operation. The mechatronic engineering approach was adopted in the design of the platform, which produced an integrated embedded system.

Open source software being implemented onboard the platform for interfacing between the platform and remote client computers is found to be easily customisable according to the requirements of one's application. A solution to the problem of nonholonomic motion constraints that concern any differential drive mobile robot was found in a nonlinear state transformation algorithm. The algorithm was implemented on an intermediate level between the interface software and the low‐level control system. The low‐level feedback control system was designed using a linear quadratic regulator design method. Simulations of this control system showed that it was robust enough to reject predetermined disturbances in system characteristics.

The application of a mobile platform specifically designed for materials handling based on the principle of the inverted pendulum has not been attempted to date.

The purpose of this paper is to propose a novel jump control method based on Two Mass Spring Damp Inverted Pendulum (TMS-DIP) model, which makes the third generation of hydraulic driven wheel-legged robot prototype (WLR-3P) achieve stable jumping.

First, according to the configuration of the WLR, a TMS-DIP model is proposed to simplify the dynamic model of the robot. Then the jumping process is divided into four stages: thrust, ascent, descent and compression, and each stage is modeled and solved independently based on TMS-DIP model. Through WLR-3P kinematics, the trajectory of the upper and lower centroids of the TMS-DIP model can be mapped to the joint space of the robot. The corresponding control strategies are proposed for jumping height, landing buffer, jumping attitude and robotic balance, so as to realize the stable jump control of the WLR.

The TMS-DIP model proposed in this paper can simplify the WLR dynamic model and provide a simple and effective tool for the jumping trajectory planning of the robot. The proposed approach is suitable for hydraulic WLR jumping control. The performance of the proposed wheel-legged jump method was verified by experiments on WLR-3P.

This work provides an effective model (TMS-DIP) for the jump control of WLR-3P. The results showed that the number of landing shock (twice) and the pitch angle fluctuation range (0.44 rad) of center of mass of the jump control method based on TMS-DIP model are smaller than those based on spring-loaded inverted pendulum model. Therefore, the TMS-DIP model makes the jumping process of WLR more stable and gentler.

The purpose of this paper is to propose an efficient and straightforward approach for system identification of a rotating single link flexible manipulator (RSLFM). Also, the achieved results are experimentally validated through identification procedure.

The proposed system identification approach is applied to a RSLFM with a tip mass. At first, the dynamic model of the system is derived using Lagrange method. Then, an efficient method is developed for identification of such a system. This method facilitates the nonlinear complicated identification problem of the RSLFM to a simplified root finding problem.

The main advantage of the developed method is to convert a complicated system identification process to a simple nonlinear equation solution. This approach uses small-size input/output data set and requires a short-time interval of data acquisition, which gives important advantages in lower computational load and lower execution time. The investigated approach is studied on experimental system identification of a single link flexible manipulator. To demonstrate this fact, the developed method is successfully applied in identification of two other mechanical systems; the inverted pendulum on a cart and the ball and beam apparatus.

In this work, the proposed identification approach has been originally applied to a RSLFM and two other mechanical examples. All obtained identification results show the performance and applicability of the developed method clearly. This approach is not restricted in using state space or transfer function. It has significant superiority in comparison with other known approaches including autoregressive with exogenous input (ARX) and Box-Jenkins (BJ).

This paper aims to propose a method to solve the problem of localization and mapping of a two-wheeled inverted pendulum (TWIP) robot on the ground using the Stereo–inertial measurement unit (IMU) system. This method reparametrizes the pose according to the motion characteristics of TWIP and considers the impact of uneven ground on vision and IMU, which is more adaptable to the real environment.

When TWIP moves, it is constrained by the ground and swings back and forth to maintain balance. Therefore, the authors parameterize the robot pose as SE(2) pose plus pitch according to the motion characteristics of TWIP. However, the authors do not omit disturbances in other directions but perform error modeling, which is integrated into the visual constraints and IMU pre-integration constraints as an error term. Finally, the authors analyze the influence of the error term on the vision and IMU constraints during the optimization process. Compared to traditional algorithms, the algorithm is simpler and better adapt to the real environment.

The results of indoor and outdoor experiments show that, for the TWIP robot, the method has better positioning accuracy and robustness compared with the state-of-the-art.

The algorithm in this paper is proposed for the localization and mapping of a TWIP robot. Different from the traditional positioning method on SE(3), this paper parameterizes the robot pose as SE(2) pose plus pitch according to the motion of TWIP and the motion disturbances in other directions are integrated into visual constraints and IMU pre-integration constraints as error terms, which simplifies the optimization parameters, better adapts to the real environment and improves the accuracy of positioning.

The purpose of this paper is to improve control performance and safety of a real two-wheeled inverted pendulum (TWIP) robot by dealing with model uncertainty and motion restriction simultaneously, which can be extended to other TWIP robotic systems.

The inequality of lumped model uncertainty boundary is derived from original TWIP dynamics. Several motion restriction conditions are derived considering zero dynamics, centripedal force, ground friction condition, posture stability, control torque limitation and so on. Sliding-mode control (SMC) and model predictive control (MPC) are separately adopted to design controllers for longitudinal and rotational motion, while taking model uncertainty into account. The reference value of the moving velocity and acceleration, delivered to the designed controller, should be restricted in a specified range, limited by motion restrictions, to keep safe.

The cancelation of model uncertainty commonly existing in real system can improve control performance. The motion commands play an important role in maintaining safety and reliability of TWIP, which can be ensured by the proposed motion restriction to avoid potential movement failure, such as slipping, lateral tipping over because of turning and large fluctuation of body.

An inequation of lumped model uncertainty boundary incorporating comprehensive errors and uncertainties of system is derived and elaborately calculated to determine the switching coefficients of SMC. The motion restrictions for TWIP robot moving in 3D are derived and used to impose constraints on reference trajectory to avoid possible instability or failure of movement.