STABILITY ANALYSIS AND ROBUST CONTROL OF A PLANAR UNDERACTUATED BIPED ROBOT

2010 ◽  
Vol 07 (04) ◽  
pp. 535-563 ◽  
Author(s):  
REZA DEHGHANI ◽  
ABBAS FATTAH
Keyword(s):  
Stability Analysis ◽  
Robust Control ◽  
Sliding Mode ◽  
Center Of Mass ◽  
Biped Robot ◽  
Gait Pattern ◽  
Research Area ◽  
Parameter Uncertainties ◽  
Stable Gait ◽  
The Stability

Stability analysis is one of the main issues in the research area of biped robots with point feet. This article develops stability analysis and robust control of a planar biped robot with point feet with one degree of underactuation. A stability analysis is presented for the bipedal motion comprising single support and impact phases by using Poincaré map for nonlinear systems. Then, the stability conditions of periodic orbits are derived and stable gait pattern is determined using an optimization process. Thereafter, a robust sliding mode control with a time-invariant feedback is proposed to track stable gait in the presence of parameter uncertainties of the biped. Proposed approach is carried out for two types of bipeds, namely, a normal model and a balanced model in which the biped center of mass located at the hip using a novel model. Energy efficiency of biped is investigated for both models. Moreover, the stability of biped motion is studied in the presence of an unexpected stair. Simulation results show the biped motion quickly converges to cyclic motion during the first gait in both models.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

An Operationally Optimized Seven Link Biped Robot Moving on Slopes

2013 ◽  
Author(s):  
Peiman Naseradinmousavi
Keyword(s):  
Simulated Annealing Algorithm ◽  
Nonlinear Modeling ◽  
Biped Robot ◽  
Gait Pattern ◽  
Critical Parameters ◽  
Modeling Process ◽  
Operational Optimization ◽  
Ankle Joints ◽  
Annealing Algorithm ◽  
The Stability

In this paper, we discuss operational optimization of a seven link biped robot using the well-known “Simulated Annealing” algorithm. Some critical parameters affecting the robot gait pattern are selected to be optimized reducing the total energy used. Nonlinear modeling process we published elsewhere is shown here for completeness. The trajectories of both the hip and ankle joints are used to plan the robot gait on slopes and undoubtedly those parameters would be the target ones for the optimization process. The results we obtained reveal considerable amounts of the energy saved for both the ascending and descending surfaces while keeping the robot stable. The stability criterion we utilized for both the modeling and then optimization is “Zero Moment Point”. A comparative study of human evolutionary gait and the operationally optimized robot is also presented.

Contact-Dependent Balance Stability of Walking Robots

2017 ◽  
Author(s):  
Carlotta Mummolo ◽  
William Z. Peng ◽  
Carlos Gonzalez ◽  
Joo H. Kim
Keyword(s):  
Stability Region ◽  
Balance Control ◽  
Center Of Mass ◽  
Biped Robot ◽  
Walking Robots ◽  
Ground Contact ◽  
Robotic Platform ◽  
Contact Configuration ◽  
The Stability ◽  
Balance Stability

A novel theoretical framework for the identification of the balance stability regions of biped systems is implemented on a real robotic platform. With the proposed method, the balance stability capabilities of a biped robot are quantified by a balance stability region in the state space of center of mass (COM) position and velocity. The boundary of such a stability region provides a threshold between balanced and falling states for the robot by including all possible COM states that are balanced with respect to a specified feet/ground contact configuration. A COM state outside of the stability region boundary is the sufficient condition for a falling state, from which a change in the specified contact configuration is inevitable. By specifying various positions of the robot’s feet on the ground, the effects of different contact configurations on the robot’s balance stability capabilities are investigated. Experimental walking trajectories of the robot are analyzed in relationship with their respective stability boundaries, to study the robot balance control during various gait phases.

scholarly journals Sliding mode learning control of uncertain nonlinear systems with Lyapunov stability analysis

2018 ◽  
Vol 41 (6) ◽  
pp. 1750-1760
Author(s):  
Erkan Kayacan
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Sliding Mode ◽  
Learning Control ◽  
System Stability ◽  
Uncertain Nonlinear Systems ◽  
System Behaviour ◽  
Lyapunov Stability Analysis ◽  
The Stability

This paper addresses the Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a type-2 neuro-fuzzy controller (T2NFC) learns system behaviour so that the T2NFC completely takes over overall control of the system in a very short time period. The stability of the sliding mode learning algorithm has been proven in the literature; however, it is restrictive for systems without overall system stability. To address this shortcoming, a novel control structure with a novel sliding surface is proposed in this paper, and the stability of the overall system is proven for nth-order uncertain nonlinear systems. To investigate the capability and effectiveness of the proposed learning and control algorithms, the simulation studies have been carried out under noisy conditions. The simulation results confirm that the developed SMLC algorithm can learn the system behaviour in the absence of any mathematical model knowledge and exhibit robust control performance against external disturbances.

Another Note on Stability of Sliding Mode Dynamics in Suppression of Fractional Chaotic Systems

2015 ◽  
Vol 743 ◽  
pp. 303-306
Author(s):  
J. Yuan ◽  
B. Shi ◽  
Yan Wang
Keyword(s):  
Stability Analysis ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
Fractional Integrator ◽  
Fractional Differential ◽  
Continuous Frequency ◽  
The Stability ◽  
Sliding Mode Dynamics

This paper revisits the stability analysis of sliding mode dynamics in suppression of a classof fractional chaotic systems by a different approach. Firstly, we convert fractional differential equationsinto infinite dimensional ordinary differential equations based on the continuous frequency distributedmodel of the fractional integrator. Then we choose a Lyapunov function candidate to proposethe stability analysis. The result applies to both the commensurate fractional systems and the incommensurateones.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

scholarly journals Robust Control Based Stability Analysis and Trajectory Tracking of Triple Link Robot Manipulator

2021 ◽  
Vol 54 (4) ◽  
pp. 641-647
Author(s):  
Mukul Kumar Gupta ◽  
Roushan Kumar ◽  
Varnita Verma ◽  
Abhinav Sharma
Keyword(s):  
Stability Analysis ◽  
Robust Control ◽  
Tracking Control ◽  
Robot Manipulator ◽  
Torque Control ◽  
Control Technique ◽  
Control Law ◽  
Worst Case ◽  
Control Techniques ◽  
The Stability

In this paper the stability and tracking control for robot manipulator subjected to known parameters is proposed using robust control technique. The modelling of robot manipulator is obtained using Euler- Lagrange technique. Three link manipulators have been taken for the study of robust control techniques. Lyapunov based approach is used for stability analysis of triple link robot manipulator. The Ultimate upper bound parameter (UUBP) is estimated by the worst-case uncertainties subject to bounded conditions. The proposed robust control is also compared with computer torque control to show the superiority of the proposed control law.

Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation

2019 ◽  
Vol 20 (8) ◽  
pp. 451-460 ◽  
Author(s):  
A. A. Kolesnikov ◽  
A. A. Kuz’menko
Keyword(s):  
Robust Control ◽  
Invariant Manifolds ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Procedure ◽  
Sliding Surface ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Laws ◽  
The Stability

Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

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