New Computational Framework for Trajectory Optimization of Higher-Order Dynamic Systems

Veeraklaew, Tawiwat; Agrawal, Sunil K.

doi:10.2514/2.4733

Cited by 28 publications

(15 citation statements)

References 4 publications

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“…The various aspects of flatness based optimal planning have been pursued by Agrawal and coworkers (Sira-Ramírez and Agrawal, 2004;Fossas et al, 2000;Ferreira and Agrawal, 1999). Dynamic optimization based on first-order and higher-order representations of a system have been compared showing substantial savings in computation (Veeraklaew and Agrawal, 2001). Preliminary results of flatness based planning of groups of autonomous vehicles were reported (Hao et al, 2003;Pledgie et al, 2002;Ferreira et al, 2000).…”

Section: Introductionmentioning

confidence: 94%

Formation Planning and Control of UGVs with Trailers

Hao

Agrawal

2005

Auton Robot

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This paper provides a framework for planning and control of formations of multiple unmanned ground vehicles with trailers to traverse between goal points in an idealized, disturbance-free environment. This framework allows on-line planning of the formations using the A* search algorithm based on current sensor data. The formation is allowed to dynamically change in order to avoid obstacles in the environment while minimizing a cost function aimed at obtaining collision-free and deadlock-free paths. Based on a feasible path for a leader of the group and the differential flatness property of a truck-tractor-trailer system, the trajectory planner satisfies the kinematic constraints of the individual vehicles while accounting for inter-vehicle collisions and path constraints. Also, optimization techniques are used to on-line change the path of the truck-tractor-trailer system. Illustrative simulations with simplified models of John Deere vehicles with trailers in formations are presented. Laboratory experiments are also performed on a 2-wheel differential drive mobile vehicle attached with a trailer cart on a flat, smooth floor using overhead cameras for precise references. The concluding section of the paper discusses some of the additional work needed to make the results applicable in a real-world environment.

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Section: Introductionmentioning

confidence: 94%

Formation Planning and Control of UGVs with Trailers

Hao

Agrawal

2005

Auton Robot

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“…As defined in ref. [13], the function space, where the extremum is sought, is 2 (0, ), x . However, such a transform gives rise to additional (velocity) variables, as well as additional (kinematical) constraints in the form x =v x [12] .…”

Section: Continuous Bolza Problemmentioning

confidence: 99%

“…The proposed approach is facilitated by two new ideas from the theory of nonlinear optimal control and the dynamic optimization, namely, the unified computational framework [12] and the extended optimality principle [13,14] . Under a set of closure conditions, it is proved that the KKT multipliers satisfy the same conditions as those obtained by collocating the costate equations of the second order, similar to the case of the costate equations of the first order [8] .…”

Section: Introductionmentioning

confidence: 99%

“…The direct approaches for the dynamic system described by a set of differential equations of the second order are still in their infancy. However, recent studies have shown their considerable advantages through some illustrative examples related to the orbit transfer and the trajectory optimization of a launch vehicle [9,10] , the tethered satellite applications [11] , and a flexible manipulator control [12][13][14] . Nevertheless, such a type of direct approaches is beyond the application of the costate estimation schemes in the literature, where the dynamic system of concern yields a set of differential equations of the first order in the state space.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamics of a mechanical system in the Lagrange space usually yields a set of differential equations of the second order, which can be discretized by using some efficient direct approaches [9][10][11][12][13][14] . The resulting NLP involves much less optimization variables and constraints than those described in the state space.…”

Section: Introductionmentioning

confidence: 99%

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Costate estimation for dynamic systems of the second order

Wen

Jin

2009

Sci. China Ser. E-Technol. Sci.

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The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear mapping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conversion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems. costate estimation, second order, pseudo-spectral method

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