Symmetries in the wheeled inverted pendulum mechanism

Gajbhiye, Sneha; Banavar, Ravi N.; Delgado, Sergio

doi:10.1007/s11071-017-3670-3

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…In the practical application process, such as home service, industrial production, transportation, space probe, etc., the WIP vehicle will inevitably encounter various obstacles, which seriously influence the implementation of related tasks [2,32,40]. Moreover, the WIP vehicle subjects to the nonholonomic constraint between the wheels and ground due to the pure rolling motion [6,11,21,34], and it is also a typical underactuated system that the number of control inputs is less than the degrees of freedom [8,14,29,37], both of which make the control of the vehicle more difficult. Therefore, developing a control method for the WIP vehicle in multi-obstacle environment not only has important theoretical meaning, but also has great practical significance.…”

Section: Introductionmentioning

confidence: 99%

WIP Vehicle Control Method Based on Improved Artificial Potential Field Subject to Multi-obstacle Environment

Yue

Ning²

2020

ITC

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This paper presents a control method for a WIP vehicle in multi-obstacle environment based on improved artificial potential field. Firstly, an improved artificial potential field (IAPF) is developed, where a safe distance is introduced to the existing repulsive potential field to solve the security issue, while the local minima can also be eliminated in the meantime. Next, an obstacle avoidance controller is designed based on the IAPF, where the nonholonomic constraint and underactuated characteristic of the WIP vehicle are fully considered, and the stability condition of the system is analyzed by means of the related control theory. Moreover, to further improve the control performance, a key parameter that play an important role in the controller is adjusted by taking advantage of fuzzy logic, and detailed analyses are given to demonstrate its necessity and effectiveness. Finally, considering a motion environment that contains dense obstacles, narrow corridor and an obstacle near the target, numerical simulations are conducted to validate the proposed method, whose results indicate that the method has a good performance to control the WIP vehicle in multi-obstacle environment.

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Section: Introductionmentioning

confidence: 99%

WIP Vehicle Control Method Based on Improved Artificial Potential Field Subject to Multi-obstacle Environment

Yue

Ning²

2020

ITC

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“…The system is underactuated since there are fewer actuating mechanisms (the drive on the wheels) than the number of configuration variables. In addition, the system has nonholonomic constraints that arise due to the pure rolling (without slipping) assumption on the wheels [2], [3] and the no side-slip condition. The WIP finds many applications that include baggage transportation, commuting and navigation [4].…”

Section: Introductionmentioning

confidence: 99%

“…Note that the WIP models available in literature (see e.g. [2], [3], [21]) consider torques as control inputs instead of the physical inputs (voltage available to DC motors). During constrained motion planning scenarios, it is essential to consider voltage and current restrictions at the trajectory design stage which necessitates the modeling of the motor dynamics.…”

Section: Introductionmentioning

confidence: 99%

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

Albert¹,

Phogat²,

Anhalt³

et al. 2018

Preprint

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The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discretetime constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

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A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

Anil,

Gajbhiye,

Mohan

2024

Intl J Robust & Nonlinear

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In this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group () framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on , we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances.

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Symmetries in the wheeled inverted pendulum mechanism

Cited by 9 publications

References 27 publications

WIP Vehicle Control Method Based on Improved Artificial Potential Field Subject to Multi-obstacle Environment

WIP Vehicle Control Method Based on Improved Artificial Potential Field Subject to Multi-obstacle Environment

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

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