Conversion of the kinematics of a car with n trailers into a chained form

Sørdalen, O.J.

doi:10.1109/robot.1993.292011

Cited by 170 publications

(110 citation statements)

References 7 publications

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“…Concerning the kinematic modeling of a wide class of wheeled robots, such as a unicycle with n − 3 trailers, [1] gives a feedback change of coordinates (z,…”

Section: B Modeling Of Nonholonomic Vehiclesmentioning

confidence: 99%

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Predictive control of chained systems: A necessary condition on the control horizon

Courtial¹,

Fruchard²,

Allibert

2012

2012 IEEE International Conference on Robotics and Automation

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Abstract-This paper deals with state feedback control of chained systems based on a Nonlinear Model Predictive Control (NMPC) strategy. Chained systems can model many common nonholonomic vehicles. We establish a relation between the degree of nonholonomy and the minimum length of the control horizon so as to make the NMPC feasible. A necessary condition on the control horizon of NMPC is given and theoretically proved whatever the dimension of the chained system considered. This relation is used to design a NMPC-based control strategy for chained systems. One of the advantages of NMPC is the capability of taking into account the constraints on state and on control variables. The theoretical results are illustrated through simulations on a (2,5) chained system, describing a car-like vehicle with one trailer. Difficult motion objectives that require a lateral displacement are considered.

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“…Concerning the kinematic modeling of a wide class of wheeled robots, such as a unicycle with n − 3 trailers, [1] gives a feedback change of coordinates (z,…”

Section: B Modeling Of Nonholonomic Vehiclesmentioning

confidence: 99%

“…can be converted into this form [1]. The stabilization problem of nonholonomic vehicles has been largely investigated in the literature [2], [3].…”

Section: Introductionmentioning

confidence: 99%

Predictive control of chained systems: A necessary condition on the control horizon

Courtial¹,

Fruchard²,

Allibert

2012

2012 IEEE International Conference on Robotics and Automation

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“…The transformation from a kinematic model of mobile robots to a chained form is presented in [28]. The system (14) can be written in a compact form asẋ…”

Section: Nonholonomic Systems In Power Formmentioning

confidence: 99%

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Laila

Astolfi

2005

Automatica

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Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed. We consider parameterized families of discrete-time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete-time model is used to design a controller for a sampled-data system. An application of our main result to time-varying periodic systems is presented, and this is used to solve a robust stabilization problem, namely to design a control law for systems in power form yielding semiglobal practical ISS (SP-ISS).

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“…The kinematic constraints are represented by firstorder differential equations, whereas the dynamic constraints are represented by second-order differential equations. There is a large body of literature on trajectory planning for nonholonomic systems with kinematic constraints, ranging from theoretical foundations [5] to practical implementations such as multi-wheeled mobile vehicles [6], [7], [8]. Underactuated systems with dynamic constraints have been approached from the controls perspective (e.g., acrobot swing-up [12]) as well as from the planning perspective (e.g., airship path planning [9]).…”

Section: Introductionmentioning

confidence: 99%

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

Nagarajan

Kantor

Hollis

2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-The ballbot is a dynamically stable mobile robot that moves on a single spherical wheel and is capable of omnidirectional movement. The ballbot is an underactuated system with nonholonomic dynamic constraints. The authors propose an offline trajectory planning algorithm that provides a class of parametric trajectories to the unactuated joint in order to reach desired static configurations of the system with regard to the dynamic constraint. The parameters of the trajectories are obtained using optimization techniques. A feedback controller is proposed that ensures accurate trajectory tracking. The trajectory planning algorithm and tracking controller are validated experimentally. The authors also extend the offline trajectory planning algorithm to a generalized case of motion between non-static configurations.

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Conversion of the kinematics of a car with n trailers into a chained form

Cited by 170 publications

References 7 publications

Predictive control of chained systems: A necessary condition on the control horizon

Predictive control of chained systems: A necessary condition on the control horizon

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

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