Model Predictive Control based on LMIs Applied to an Omni-Directional Mobile Robot

Araujo, H. X.; Conceição, André Gustavo Scolari; Oliveira, Gustavo H. C.; Pitanga, Jonatas R.

doi:10.3182/20110828-6-it-1002.03696

Cited by 18 publications

(12 citation statements)

References 12 publications

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“…The works [6,7,12,22,24,28,31,32,43] concern two-wheeled robots, and work [6] concerns inverted pendulum robot. In turn, works [2,5,10,20,21,29,38] describe three-wheeled omnidirectional robots, whereas [1,4,18,35], three-wheeled robots with two fixed driven wheels and castor. Works [13,17,27,30] cover research involving fourwheeled robots of car-like steering type, the work [11] is concerned with differentially driven four-wheeled robot with two wheels driven and two castors, whereas works [9,45,46] describe four-wheeled omnidirectional robot.…”

Section: Wheeled Mobile Robots and Slippagementioning

confidence: 99%

“…In several works, topic of methods of compensation of this kind of disturbances for three-wheeled omnidirectional robots was discussed. Detailed description of controller structure for the case of compensation of friction results for robots like that can be found in works: [2,5,9,28]. In particular, in work [2] example description of model transformations is contained, where in a separate matrix dependencies of measurable (or modelled) disturbances are given.…”

Section: Wheeled Mobile Robots and Slippagementioning

confidence: 99%

“…In the reviewed literature concerning predictive control of WMRs, in the example works [2,5,11,17,18,21,22,28,44,46] authors mainly use the second approach, because it is more promising for more effective solution of the problem.…”

Section: Constraints Of Controlled Objects and Optimization Criteriamentioning

confidence: 99%

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State of the Art in Predictive Control of Wheeled Mobile Robots

Harasim

Trojnacki

2016

JAMRIS

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The paper is concerned with the problem of tracking control of wheeled mobile robots (WMRs) using predictive control systems. Various kinematic structures of WMRs important from the point of view of motion control are discussed. A hierarchical approach to the problem of motion control of this kind of robots is presented. The problems of trajectory tracking and path following control of WMRs are briefly discussed. The methods of predictive control of WMRs are described in detail and the following aspects relevant to predictive control are considered: kinematic structures of robots, slip of wheels and its compensation, assumed constraints, methods of optimization of the objective function, problems of model nonlinearity, linearization and discretization, stability of the control system and use of the state observers.

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Section: Wheeled Mobile Robots and Slippagementioning

confidence: 99%

Section: Wheeled Mobile Robots and Slippagementioning

confidence: 99%

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State of the Art in Predictive Control of Wheeled Mobile Robots

Harasim

Trojnacki

2016

JAMRIS

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“…In [24], the passivity-based controller based on "PD+" approach was proposed to solve the global trajectory tracking control problem using only position measurements. Many researchers applied the model-predictive control design to solve the trajectory tracking problem [8,26,29].…”

Section: Introductionmentioning

confidence: 99%

On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

Andreev¹,

Peregudova²

2020

Nelin. Dinam.

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This paper addresses the trajectory tracking control design of an omnidirectional mobile robot with a center of mass displaced from the geometrical center of the robot platform. Due to the high maneuverability provided by omniwheels, such robots are widely used in industry to transport loads in narrow spaces. As a rule, the center of mass of the load does not coincide with the geometric center of the robot platform. This makes the trajectory tracking control problem of a robot with a displaced center of mass relevant. In this paper, two controllers are constructed that solve the problem of global trajectory tracking control of the robot. The controllers are designed based on the Lyapunov function method. The main difficulty in applying the Lyapunov function method for the trajectory tracking control problem of the robot is that the time derivative of the Lyapunov function is not definite negative, but only semidefinite negative. Moreover, the LaSalle invariance principle is not applicable in this case since the closed-loop system is a nonautonomous system of differential equations. In this paper, it is shown that the quasi-invariance principle for nonautonomous systems of differential equations is much convenient for the asymptotic stability analysis of the closed-loop system. Firstly, we construct an unbounded state feedback controller such as proportional-derivative term plus feedforward. As a result, the global uniform asymptotic stability property of the origin of the closed-loop system has been proved. Secondly, we find that, if the damping forces of the robot are large enough, then the saturated position output feedback controller solves the global trajectory tracking control problem without velocity measurements. The effectiveness of the proposed controllers has been verified through simulation tests. Namely, a comparative analysis of the bounded controller obtained and the well-known "PD+" like control scheme is carried out. It is shown that the approach proposed in this paper saves energy for control inputs. A. S. Andreev, O. A. PeregudovaBesides, a comparative analysis of the bounded controller and its analogue constructed earlier in a cylindrical phase space is carried out. It is shown that the controller provides lower values for the root mean square error of the position and velocity of the closed-loop system.

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“…In [20], a model-predictive trajectory-tracking controller, which used linearized tracking-error dynamics to predict future system behavior, was presented. In [21], a state feedback MPC method was proposed and applied for trajectory tracking of a three-wheeled OMR. The cost function in the proposed MPC method is constructed over finite horizon and is optimized in the linear matrix inequalities (LMI) framework.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Tracking of an Omni-Directional Wheeled Mobile Robot Using a Model Predictive Control Strategy

et al. 2018

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This paper addresses trajectory tracking of an omni-directional mobile robot (OMR) with three mecanum wheels and a fully symmetrical configuration. The omni-directional wheeled robot outperforms the non-holonomic wheeled robot due to its ability to rotate and translate independently and simultaneously. A kinematics model of the OMR is established and a model predictive control (MPC) algorithm with control and system constraints is designed to achieve point stabilization and trajectory tracking. Simulation results validate the accuracy of the established kinematics model and the effectiveness of the proposed MPC controller.

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Model Predictive Control based on LMIs Applied to an Omni-Directional Mobile Robot

Cited by 18 publications

References 12 publications

State of the Art in Predictive Control of Wheeled Mobile Robots

State of the Art in Predictive Control of Wheeled Mobile Robots

On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

Trajectory Tracking of an Omni-Directional Wheeled Mobile Robot Using a Model Predictive Control Strategy

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