Jaume Franch
Universitat Politecnica de Catalunya, Matemàtica Aplicada 4, Faculty Member
It is well known that given a controllable system, addition of new actuators cannot make the system to loose the controllability property. For linear systems, since controllability is equivalent to differential flatness, the latter... more
It is well known that given a controllable system, addition of new actuators cannot make the system to loose the controllability property. For linear systems, since controllability is equivalent to differential flatness, the latter property cannot be lost by addition of new inputs. However, this is not true for nonlinear systems. In this paper, we investigate under which conditions systems that are perturbed by addition of new inputs retain the property of being linearizable by static feedback linearization. Some sufficient conditions and a necessary one are given. The theory is illustrated with some examples.
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Gives a bound on the number of integrators needed to linearize a control system with an arbitrary number of inputs. Although some work has been done in this direction in Sluis and Tilbury (1996), our bound improves the existing results... more
Gives a bound on the number of integrators needed to linearize a control system with an arbitrary number of inputs. Although some work has been done in this direction in Sluis and Tilbury (1996), our bound improves the existing results for systems with four or more inputs. The bound for two input systems is the same as the one that appeared in the above mentioned paper.
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ABSTRACT The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory... more
ABSTRACT The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally inexpensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. In this paper, nonholonomic rate constraints for free-floating planar open-chain robots are studied together with auxiliary joint variable constraints to determine design conditions under which the system exhibits differential flatness. Sufficient conditions are derived for existence of flatness and are illustrated by examples.
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... Rathinam, M and Murray, RM. 1998. Configuration flatness of lagrangian systems underactuated by one control. SIAM J. Cont. Optim. ... Rathinam, M and Murray, RM. 1998. Configuration flatness of lagrangian systems underactuated by one... more
... Rathinam, M and Murray, RM. 1998. Configuration flatness of lagrangian systems underactuated by one control. SIAM J. Cont. Optim. ... Rathinam, M and Murray, RM. 1998. Configuration flatness of lagrangian systems underactuated by one control. SIAM J. Cont. Optim. ...
Research Interests: Mathematics, Applied Mathematics, Computer Science, Control, Path planning, and 13 moreDifferential Equations, Control system, Computation, ROBOT, Feedback Control, Feedback, Intelligent robots, Holonomic constraints, Path Planning, Boolean Satisfiability, Dynamic System, Electrical And Electronic Engineering, and Angular Momentum
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Page 1. Proceedings of the 2003 IEEEIRSJ Intl. Conference on Intelligent Robots and Systems Las Vegas, Nevada ' October 2003 Design of Differentially Flat Planar Space Robots: A Step Forward their Planning and Control ...
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ABSTRACT This paper investigates when a 2 degree-of-freedom PRRRP closed-chain system with a single actuator is both strongly accessible and feedback linearizable. It is demonstrated that for certain choices of mass distribution and... more
ABSTRACT This paper investigates when a 2 degree-of-freedom PRRRP closed-chain system with a single actuator is both strongly accessible and feedback linearizable. It is demonstrated that for certain choices of mass distribution and addition of springs, an under-actuated 2 DOF PRRRP system is static feedback linearizable, i.e., also differentially flat.
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Abstract-The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, ie, are nonintegrable rate equations. If... more
Abstract-The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, ie, are nonintegrable rate equations. If the base of the free-floating robot ...
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This paper demonstrates that for certain choices of mass distribution and addition of springs, an underactuated two-degree-of-freedom (2-DOF) \bm PRRRP system is static feedback linearizable, i.e., differentially flat as well. This paper... more
This paper demonstrates that for certain choices of mass distribution and addition of springs, an underactuated two-degree-of-freedom (2-DOF) \bm PRRRP system is static feedback linearizable, i.e., differentially flat as well. This paper is original and provides a ground breaking study in underactuated dynamical systems.
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New bounds on the number of integrators ... This paper gives a bound on the number of integrators needed to linearize a control system with an arbitrary number of inputs. Although some work has been done in this direction in [14], our... more
New bounds on the number of integrators ... This paper gives a bound on the number of integrators needed to linearize a control system with an arbitrary number of inputs. Although some work has been done in this direction in [14], our bound improves the existing results for ...
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This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system's dynamic model. The theory of differential flatness is used as the basic approach in these... more
This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system's dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize ...
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In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is... more
In this paper, the dynamic model of a wheeled inverted pendulum
(e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability
and feedback linearizability point of view. First, a dynamic model of this underactuated
system is derived with respect to the wheel motor torques as inputs
while taking the nonholonomic no-slip constraints into considerations.
This model is compared with the previous models derived for similar systems.
The strong accessibility condition is checked and the maximum relative
degree of the system is found. Based on this result, a partial feedback
linearization of the system is obtained and the internal dynamics equations
are isolated. The resulting equations are then used to design two novel controllers.
The first one is a two-level velocity controller for tracking vehicle
orientation and heading speed set-points, while controlling the vehicle pitch
(pendulum angle from the vertical) within a specified range. The second
controller is also a two-level controller which stabilizes the vehicle’s position
to the desired point, while again keeping the pitch bounded between
specified limits. Simulation results are provided to show the efficacy of the
controllers using realistic data.
(e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability
and feedback linearizability point of view. First, a dynamic model of this underactuated
system is derived with respect to the wheel motor torques as inputs
while taking the nonholonomic no-slip constraints into considerations.
This model is compared with the previous models derived for similar systems.
The strong accessibility condition is checked and the maximum relative
degree of the system is found. Based on this result, a partial feedback
linearization of the system is obtained and the internal dynamics equations
are isolated. The resulting equations are then used to design two novel controllers.
The first one is a two-level velocity controller for tracking vehicle
orientation and heading speed set-points, while controlling the vehicle pitch
(pendulum angle from the vertical) within a specified range. The second
controller is also a two-level controller which stabilizes the vehicle’s position
to the desired point, while again keeping the pitch bounded between
specified limits. Simulation results are provided to show the efficacy of the
controllers using realistic data.
Research Interests: Engineering, Mechanical Engineering, Computer Science, Accessibility, Modeling, and 15 moreControllability, Mobile Robots, Feedback, Inverted Pendulum, Mobile Robot, Linearization, Nonlinear system, direct Lyapunov method, Dynamic Model of WSN, Feedback Linearization, Electrical And Electronic Engineering, Double Inverted Pendulum, dynamic model, Nonholonomic System, and Lyapunov method
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Optimal solution of classes of Mayer problems with feedback linearizable state equations possess unique structures. A number of special numerical algorithms are available to construct their optimal solution. In this paper, we investigate... more
Optimal solution of classes of Mayer problems with feedback linearizable state equations possess unique structures. A number of special numerical algorithms are available to construct their optimal solution. In this paper, we investigate the following question: What classes of optimal control Lagrange problems can be transformed to Mayer problems with feedback linearized state equations?. Using the results of this question, the structure of the optimal solution for a Mayer problem can be extended to the solution of the original Lagrange problem.
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... 2. Se us enviara inmediatament un correu a la vostra adreça electrónica. 3. Llegiu el correu i feu clic en l'enllaç web indos. 4. Es confirmara el vostre compte i podreu entrar-hi. 5. Llavors, 5eleccioneu el curs en el qual voleu... more
... 2. Se us enviara inmediatament un correu a la vostra adreça electrónica. 3. Llegiu el correu i feu clic en l'enllaç web indos. 4. Es confirmara el vostre compte i podreu entrar-hi. 5. Llavors, 5eleccioneu el curs en el qual voleu participar. ...
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Aquest article estudia el c` alcul de les sortides planes mitjançant la forma normal de Goursat del sistema de Pfaff associat a qualsevol sistema de control en variables d'estat. L'algorisme consta de tres passos: i) transformació... more
Aquest article estudia el c` alcul de les sortides planes mitjançant la forma normal de Goursat del sistema de Pfaff associat a qualsevol sistema de control en variables d'estat. L'algorisme consta de tres passos: i) transformació del sistema de control en el seu sistema de Pfaff equivalent; ii) c` alcul de la forma normal de Goursat; iii) reescriptura de les equacions en les noves variables d'estat. Aquí, una realimentació simplifica les equacions i, per tant, les sortides planes es calculen de manera senzilla. L'algorisme s'aplica a un vehicle amb rodes extensibles. Gràcies a la propietat de planitud diferencial, s'obtenen les trajectòries entre dos punts donats. Abstract (ENG) This paper is devoted to computation of flat outputs by means of the Goursat normal form of the Pfaffian system associated to any control system in state space form. The algorithm consists of three steps: i) transformation of the system into its Pfaffian equivalent; ii) computation o...
This communication deals with the problem of linearization by prolongations of two-input driftless systems. For general two-input systems, the number of computations needed to check if a system is linearizable by prolongations is quite... more
This communication deals with the problem of linearization by prolongations of two-input driftless systems. For general two-input systems, the number of computations needed to check if a system is linearizable by prolongations is quite large. However, for driftless systems, the conditions presented in this paper require very few computations. The methodology is illustrated for some engineering systems which fulfill these conditions, e.g., a unicycle, a planar robot, and a hopping robot.
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This communication deals with the problem of linearization by prolongations of two-input driftless systems. For general two-input systems, the number of computations needed to check if a system is linearizable by prolongations is quite... more
This communication deals with the problem of linearization by prolongations of two-input driftless systems. For general two-input systems, the number of computations needed to check if a system is linearizable by prolongations is quite large. However, for driftless systems, the conditions presented in this paper require very few computations. The methodology is illustrated for some engineering systems which fulfill these conditions, e.g., a unicycle, a planar robot, and a hopping robot.
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This paper proposes a trajectory controller and a trajectory generation algorithm for an Ackerman vehicle. The definition of the system is based on a dynamic model which makes it possible to describe it in terms of the input signals... more
This paper proposes a trajectory controller and a trajectory generation algorithm for an Ackerman vehicle. The definition of the system is based on a dynamic model which makes it possible to describe it in terms of the input signals normally reacheable for the driver: the torque of the engine related with the level of the gas pedal, and the movement of the steering wheel. This way, this control method can be implemented on any existing vehicle with minimum changes. For handling the nonlinearities present in the system, the mathematical description of the Ackerman vehicle is arranged in such a way that it fulfills the flatness conditions, making it possible to apply dynamic linearization. Another benefit of the proposed flat description is the close relationship between the flat outputs and the geometrical description of the path, so that the development of the control law for reaching any point in the surroundings of the vehicle is straightforward. In this connection, the trajectory...
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Research Interests: Mechanical Engineering, Accessibility, Modeling, Vehicle Dynamics, Stability, and 17 moreControllability, Mobile Robots, Nonlinear Systems, Feedback, Inverted Pendulum, Mobile Robot, Position Control, Wheel, Nonlinear system, direct Lyapunov method, Dynamic Model of WSN, Point of View, Feedback Linearization, Electrical And Electronic Engineering, Speed Control, Underactuation, and Underactuated System
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Research Interests: Mechanical Engineering, Robotics, Applied Mathematics, Nonlinear Programming, Motion control, and 16 moreAutomatic Control, Path planning, Non Linear Programming, Mobile Robots, Trajectory Planning, Momentum, Historic conservation law, Wheel, Space Robotics, Path Planning, Inercia, Electrical And Electronic Engineering, Inertia, Open-loop, Space Robots, and Underactuation
ABSTRACT The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory... more
ABSTRACT The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally inexpensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. In this paper, nonholonomic rate constraints for free-floating planar open-chain robots are studied together with auxiliary joint variable constraints to determine design conditions under which the system exhibits differential flatness. Sufficient conditions are derived for existence of flatness and are illustrated by examples.
Research Interests:
Abstract-The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, ie, are nonintegrable rate equations. If... more
Abstract-The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, ie, are nonintegrable rate equations. If the base of the free-floating robot ...
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^ (k) + pk01^ (k01) + 111 + p1_^ + p0^ = Fk01g(t) (k01) + 111 + F1 _g(t) + F0g(t) (36) where the numbers p0; p1; ... ; pk01 are the coefficients of the charac-teristic polynomial (17), and the matrices Fk01; ... ; F1; F0 2 ... + 111 +... more
^ (k) + pk01^ (k01) + 111 + p1_^ + p0^ = Fk01g(t) (k01) + 111 + F1 _g(t) + F0g(t) (36) where the numbers p0; p1; ... ; pk01 are the coefficients of the charac-teristic polynomial (17), and the matrices Fk01; ... ; F1; F0 2 ... + 111 + (p1I + QF1 0 F0) _g(t)+(p0I + QF0)g(t) = 0 (k) + pk01 (k01) + ...
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ABSTRACT It is well known that a controllable nonlinear system will retain its controllabality when new actuator inputs are added to it. In this article, we ask the question if a system, linearisable by static or dynamic feedback, will... more
ABSTRACT It is well known that a controllable nonlinear system will retain its controllabality when new actuator inputs are added to it. In this article, we ask the question if a system, linearisable by static or dynamic feedback, will retain this property when new actuator inputs are added to it. Alternatively, a system may be linearisable after removing one or more inputs from it. This question is important in the design of robotic systems from the perspective of trajectory planning and control, specially if they are under-actuated. The goals of this article are as follows: (i) using counter examples, we first show that feedback linearisability may not be preserved when new inputs are added to a robotic system, (ii) sufficient conditions are determined when a system will retain this property under the addition of new inputs. The theory is illustrated through some examples from the robotics field.