Simultaneous tracking and stabilization of an omnidirectional mobile robot in polar coordinates: a unified control approach

Robotica ◽  
2009 ◽  
Vol 27 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Hsu-Chih Huang ◽  
Ching-Chih Tsai
Keyword(s):  
Mobile Robot ◽  
Feedback Linearization ◽  
Control Method ◽  
Kinematic Model ◽  
Path Following ◽  
Polar Space ◽  
Polar Coordinates ◽  
Control Approach ◽  
Omnidirectional Mobile Robot ◽  
Omnidirectional Wheels

SUMMARYThis paper presents a polar-space kinematics control method to achieve simultaneous tracking and stabilization for an omnidirectional wheeled mobile robot with three independent driving omnidirectional wheels equally spaced at 120° from one another. The kinematic model of the robot in polar coordinates is presented. With the kinematic model, a kinematic control method based on feedback linearization is proposed in order to achieve simultaneous tracking and stabilization. The proposed method is easily extended to address the path following problem. Computer simulations and experimental results are presented to show the effectiveness and usefulness of the proposed control method at slow speeds.

scholarly journals A Nonlinear H-infinity Control Approach for Autonomous Truck and Trailer Systems

2020 ◽  
Vol 08 (01) ◽  
pp. 49-69 ◽  
Author(s):  
Gerasimos Rigatos ◽  
Pierluigi Siano ◽  
Patrice Wira ◽  
Krishna Busawon ◽  
Richard Binns
Keyword(s):  
Autonomous Vehicles ◽  
Control Method ◽  
Kinematic Model ◽  
Taylor Series Expansion ◽  
Time Instant ◽  
Algebraic Riccati Equation ◽  
Control Loop ◽  
H Infinity ◽  
Control Approach ◽  
H Infinity Control

A nonlinear optimal control method is developed for autonomous truck and trailer systems. Actually, two cases are distinguished: (a) a truck and trailer system that is steered by the front wheels of its truck, (b) an autonomous fire-truck robot that is steered by both the front wheels of its truck and by the rear wheels of its trailer. The kinematic model of the autonomous vehicles undergoes linearization through Taylor series expansion. The linearization is computed at a temporary operating point that is defined at each time instant by the present value of the state vector and the last value of the control inputs vector. The linearization is based on the computation of Jacobian matrices. The modeling error due to approximate linearization is considered to be a perturbation that is compensated by the robustness of the control scheme. For the approximately linearized model of the autonomous vehicles an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. The stability of the control loop is confirmed through Lyapunov analysis. It is shown that the control loop exhibits the H-infinity tracking performance which implies elevated robustness against modeling errors and external disturbances. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven. Finally, to implement state estimation-based control for the autonomous vehicles, through the processing of a small number of sensor measurements, the H-infinity Kalman Filter is proposed.

scholarly journals Predictive Control of Mobile Robot Using Kinematic and Dynamic Models

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Manel Mendili ◽  
Faouzi Bouani
Keyword(s):  
Optimal Control ◽  
Mobile Robot ◽  
Predictive Control ◽  
Dynamic Models ◽  
Kinematic Model ◽  
Performance Criterion ◽  
Control Sequence ◽  
Omnidirectional Mobile Robot ◽  
Quadratic Performance ◽  
Predictive Controllers

This paper presents a predictive control of omnidirectional mobile robot with three independent driving wheels based on kinematic and dynamic models. Two predictive controllers are developed. The first is based on the kinematic model and the second is founded on the dynamic model. The optimal control sequence is obtained by minimizing a quadratic performance criterion. A comparison has been done between the two controllers and simulations have been done to show the effectiveness of the predictive control with the kinematic and the dynamic models.

scholarly journals Suboptimal Omnidirectional Wheel Design and Implementation

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 865
Author(s):  
Jordi Palacín ◽  
David Martínez ◽  
Elena Rubies ◽  
Eduard Clotet
Keyword(s):  
Mobile Robot ◽  
Suspension System ◽  
Final Conclusion ◽  
Manufacturing Cost ◽  
Omnidirectional Mobile Robot ◽  
Planar Surfaces ◽  
Motion System ◽  
Contact Discontinuities ◽  
Passive Suspension System ◽  
Omnidirectional Wheels

The optimal design of an omnidirectional wheel is usually focused on the minimization of the gap between the free rollers of the wheel in order to minimize contact discontinuities with the floor in order to minimize the generation of vibrations. However, in practice, a fast, tall, and heavy-weighted mobile robot using optimal omnidirectional wheels may also need a suspension system in order to reduce the presence of vibrations and oscillations in the upper part of the mobile robot. This paper empirically evaluates whether a heavy-weighted omnidirectional mobile robot can take advantage of its passive suspension system in order to also use non-optimal or suboptimal omnidirectional wheels with a non-optimized inner gap. The main comparative advantages of the proposed suboptimal omnidirectional wheel are its low manufacturing cost and the possibility of taking advantage of the gap to operate outdoors. The experimental part of this paper compares the vibrations generated by the motion system of a versatile mobile robot using optimal and suboptimal omnidirectional wheels. The final conclusion is that a suboptimal wheel with a large gap produces comparable on-board vibration patterns while maintaining the traction and increasing the grip on non-perfect planar surfaces.

scholarly journals Analysis, Design, and Control of an Omnidirectional Mobile Robot in Rough Terrain

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Martin Udengaard ◽  
Karl Iagnemma
Keyword(s):  
Mobile Robot ◽  
Control Method ◽  
Optimization Method ◽  
Contact Angles ◽  
Design Guidelines ◽  
Rough Terrain ◽  
Uneven Terrain ◽  
Omnidirectional Mobile Robot ◽  
Subsystem Design ◽  
And Control

An omnidirectional mobile robot is able, kinematically, to move in any direction regardless of current pose. To date, nearly all designs and analyses of omnidirectional mobile robots have considered the case of motion on flat, smooth terrain. In this paper, an investigation of the design and control of an omnidirectional mobile robot for use in rough terrain is presented. Kinematic and geometric properties of the active split offset caster drive mechanism are investigated along with system and subsystem design guidelines. An optimization method is implemented to explore the design space. The use of this method results in a robot that has higher mobility than a robot designed using engineering judgment. A simple kinematic controller that considers the effects of terrain unevenness via an estimate of the wheel-terrain contact angles is also presented. It is shown in simulation that under the proposed control method, near-omnidirectional tracking performance is possible even in rough, uneven terrain.

Discrete and Analytic Model Predictive Control for Path Following of Underactuated Ships

2009 ◽  
Author(s):  
Xiaofei Wang ◽  
Zaojian Zou ◽  
Tieshan Li ◽  
Weilin Luo
Keyword(s):  
Model Predictive Control ◽  
State Space ◽  
Predictive Control ◽  
Feedback Linearization ◽  
Control Method ◽  
State Space Model ◽  
Path Following ◽  
Analytic Model ◽  
Space Model ◽  
Path Following Control

The control problem of underactuated surface ships and underwater vehicles has attracted more and more attentions during the last years. Path following control aims at forcing the vehicles to converge and follow a desired path. Path following control of underactuated surface ships or underwater vehicles is an important issue to study nonlinear systems control, and it is also important in the practical implementation such as the guidance and control of marine vehicles. This paper proposes two nonlinear model predictive control algorithms to force an underactuated ship to follow a predefined path. One algorithm is based on state space model, the other is based on analytic model predictive control. In the first algorithm, the state space GPC (Generalized Predictive Control) method is used to design the path-following controller of underactuated ships. The nonlinear path following system of underactuated ships is discretized and re-arranged into state space model. Then states are augmented to get the new state space model with control increment as input. Thus the problem is becoming a typical state space GPC problem. Some characters of GPC such as cost function, receding optimization, prediction horizon and control horizon occur in the design procedure of path-following controller. The control law is derived in the form of control increment. In the second algorithm, an analytic model predictive control algorithm is used to study the path following problem of underactuated ships. In this path-following algorithm, the output-redefinition combined heading angle and cross-track error is introduced. As a result, the original single-input multiple-output (SIMO) system is transformed into an equivalent single-input single-output (SISO) system. For the transformed system, we use the analytic model predictive control method to get path-following control law in the analytical form. The analytic model predictive controller can be regarded as special feedback linearization method optimized by predictive control method. It provides a systematic method to compute control parameters rather than by try-and-error method which is often used in the exact feedback linearization control. Relative to GPC, the analytic model predictive control method provides an analytic optimal solution and decreases the computational burden, and the stability of closed-loop system is guaranteed. The path-following system of underactuated ships is guaranteed to follow and stabilize onto the desired path. Numerical simulations demonstrate the validity of the proposed control laws.

scholarly journals Restriction of Transverse Feedback Linearization for Piecewise Linear Paths

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Gildeberto de Souza Cardoso ◽  
Leizer Schnitman ◽  
José Valentim dos Santos Filho ◽  
Luiz Carlos Simões Soares Júnior
Keyword(s):  
Mobile Robot ◽  
Feedback Linearization ◽  
Piecewise Linear ◽  
Domain Of Attraction ◽  
Path Following ◽  
Transverse Feedback Linearization

This work presents a path-following controller for a unicycle robot. The main contribution of this paper is to demonstrate the restriction of transverse feedback linearization (TFL) to obtuse angles on piecewise linear paths. This restriction is experimentally demonstrated on a Kobuki mobile robot, where it is possible to observe, as a result of the limitation of the TFL, the convergence to another domain of attraction.

Quaternion-Based Control of Acrobatic Quadrotor With Trajectory Following

2020 ◽  
Author(s):  
Haowen Liu ◽  
Bingen Yang
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Control Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Path Following ◽  
Differential Flatness ◽  
Reference Trajectory ◽  
Control Approach ◽  
Trajectory Following

Abstract For an unmanned aerial vehicle (UAV), its navigation in terrains can be quite challenging. To reach the destination within the required time, the maneuver of the quadrotor must behave aggressively. During this aggressive maneuvering, the quadrotor can experience singularities in the yaw-direction rotation. Thus, it is essentially important to develop a mathematical model and control method that can avoid singularities while enabling such an aggressive maneuver. In our previous effort, we demonstrated a vertical loop aggressive maneuver performed by a quadrotor UAV, which utilizes the controlled loop path following (CLPF) method. As found in this work, conventional modeling and tracking control method may not be good enough if specific requirements, such as fast coasting speed and sharp turns, are imposed. The numerical simulation by singularity-free modeling and the CLPF method enables a quadrotor to be operated in aggressive maneuverability with features like automatic flipping and precise trajectory following. The current research extends the maneuverability of a quadrotor by using a different and more capable control approach. More complex trajectories are used to test this new control method. In this paper, a quadrotor is used to demonstrate the capability of the proposed control method in delivering an aggressive and singularity-free maneuver. A quaternion-based mathematical model of the quadrotor is derived to avoid the singularities of rotation during the aggressive maneuvers. At the same time, a new control method, namely the full quaternion differential flatness (FQDF) method, is developed for quadrotors to combat the requirement of a fast maneuver in three-dimensional space. The FQDF method, which makes use of full quaternion modeling and differential flatness, enables the quadrotor to react to the reference trajectory timely and to exhibit aggressive rotation without any singularity. Also, the singularities resulting from the heading direction can be resolved by a new algorithm. The FQDF method is compared with the reference literature’s methods and is tested in different trajectories from the ones in the previous studies. The numerical simulation demonstrates the aggressive maneuverability and computational efficiency of the proposed control method.

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