# Multidimensional Path Tracking With Global Least Squares Solution

Research output: Contribution to conference › Paper › peer-review

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**Multidimensional Path Tracking With Global Least Squares Solution.** / Handler, Johannes; Harker, Matthew; Rath, Gerhard.

Research output: Contribution to conference › Paper › peer-review

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*Multidimensional Path Tracking With Global Least Squares Solution*. 6267-6272. Paper presented at 21st IFAC World Congress (Virtual), Berlin, Germany.

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TY - CONF

T1 - Multidimensional Path Tracking With Global Least Squares Solution

AU - Handler, Johannes

AU - Harker, Matthew

AU - Rath, Gerhard

PY - 2020

Y1 - 2020

N2 - In this paper, a new method for model based optimal tracking control is presented.The special composition of the cost functional leads to design parameters for constraining thesolution so as to ensure that machine limitations are not violated. By minimizing the costfunctional with the calculus of variations, or more precisely the Euler-Lagrange equations, thestate space representation of the system dynamics is transformed into an augmented statespace representation describing the optimal tracking dynamics. The optimal control input isnumerically calculated by solving the set of dierential equations, given by the augmented statespace system, globally with a specialized least-squares solver. The general control approach isdemonstrated on an underactuated crane-like system with xed load hoisting length operatingin the horizontal plane. In this case the introduced design parameters determine the tradeo between the cost of tracking accuracy and the cost of using large values of crane speedand acceleration. The potential of the proposed control scheme is proven by both simulationand experimental tests. The multibody simulation is carried out with the software SimscapeMultibodyTM. For the experimental verication an industrial robot is used whose end eectoronly moves in a horizontal plane to imitate the trolley of an overhead crane.

AB - In this paper, a new method for model based optimal tracking control is presented.The special composition of the cost functional leads to design parameters for constraining thesolution so as to ensure that machine limitations are not violated. By minimizing the costfunctional with the calculus of variations, or more precisely the Euler-Lagrange equations, thestate space representation of the system dynamics is transformed into an augmented statespace representation describing the optimal tracking dynamics. The optimal control input isnumerically calculated by solving the set of dierential equations, given by the augmented statespace system, globally with a specialized least-squares solver. The general control approach isdemonstrated on an underactuated crane-like system with xed load hoisting length operatingin the horizontal plane. In this case the introduced design parameters determine the tradeo between the cost of tracking accuracy and the cost of using large values of crane speedand acceleration. The potential of the proposed control scheme is proven by both simulationand experimental tests. The multibody simulation is carried out with the software SimscapeMultibodyTM. For the experimental verication an industrial robot is used whose end eectoronly moves in a horizontal plane to imitate the trolley of an overhead crane.

M3 - Paper

SP - 6267

EP - 6272

Y2 - 12 July 2020 through 17 July 2020

ER -