A path space approach to nonholonomic motion planning in the presence of obstacles

Divelbiss, A.W.; Wen, John T.

doi:10.1109/70.585905

Cited by 106 publications

(53 citation statements)

References 25 publications

(21 reference statements)

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“…The unconstrained non-holonomic motion planning with Φ 0 = 0 has been also analysed in works [1,11,12,49]. Although studies [26,37] involve the performance index in trajectory planning, the gradient of the Hamiltonian in [26,37] is projected onto the null-subspace of the Jacobian what does not even guarantee an instantaneous sub-optimal solution in the case of the con-flict of the kinematic tasks.…”

Section: Theoremmentioning

confidence: 99%

“…dt with performance index (11). To use the negative formulation of Pontryagin's Maximum Principle [14,18,23], we assume that a certain admissible control v 0 = v 0 (t), that is, satisfying relations (2) but not necessarily (3) and (4), is known.…”

Section: Generation Of Optimal Trajectory Of the Non-holonomic Systemmentioning

confidence: 99%

“…As is known, the Hamiltonian-based approaches provide, in fact, only stationary solutions which may not necessarily be optimal ones. Moreover, in the case of classic (constraint-free) non-holonomic motion planning problems analysed and solved in the majority of works by means of the pseudo-inverses of Jacobian matrices [1,11,12,26,37,49,50], our control scheme is significantly simplified in such a way that it does not require computation of inverse or pseudo-inverse of the Jacobian what also results in numerical stability of the approach. The technique of convergence proof for the proposed algorithms is different from those known in the literature and is based on searching for limit trajectory whose existence is theoretically ensured.…”

Section: Introductionmentioning

confidence: 99%

“…According to the discrete grid-based artificial potential field method, a global collision-free path planning of a cooperative cable parallel robot for multiple mobile cranes was presented in [58]. However, the graph search methods based on state space decomposition can be computationally both time-consuming (due to preprocessing of the continuous work space into a suitable graph) and complicated particularly for complex non-holonomic systems such as a tractor pulling the two or more trailers [11]. The second approach applying the Jacobian motion planning algorithms is based on so-called continuation method inspired by Wazewski [54].…”

Section: Introductionmentioning

confidence: 99%

“…It was introduced to robotics by Sussmann [48]. Jacobian algorithms have been developed theoretically in [8,9] and applied to non-holonomic systems in [1,11,12,26,37,[49][50][51]. The augmented motion planning techniques such as the extended Jacobian [2,4] or the configuration control proposed in [45] were adopted to non-holonomic systems in work [50].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The planning of optimal motions of non-holonomic systems

Galicki

2017

Nonlinear Dyn

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A new method to the planning of optimal motions of the non-holonomic systems is presented. It is based on a non-classical formulation of the Pontryagin Maximum Principle given in variational form, which handles efficiently various control and/or statedependent constraints. They arise naturally due to both physical limits of the actuators of the non-holonomic systems and potential existence of obstacles in the workspace. The method proposed here provides continuous solutions in infinite-dimensional control space. It seems to be in contrast to majority of known optimization algorithms which project infinite-dimensional control space into finite-dimensional one and then apply techniques of linear and/or nonlinear programming, thus resulting only in near-optimal trajectories. Moreover, the offered control schemes do not require computation of inverse or pseudo-inverse of the Jacobian in the case of classic non-holonomic motion planning what also results in numerical stability of our approach. The performance of the proposed control strategies is illustrated through computer simulations for a chosen class of non-holonomic structures operating in both an obstacle-free workspace and a workspace including obstacles. Numerical comparison of our control scheme with the representative algorithms known from the literature is also given.

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Section: Theoremmentioning

confidence: 99%

Section: Generation Of Optimal Trajectory Of the Non-holonomic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The planning of optimal motions of non-holonomic systems

Galicki

2017

Nonlinear Dyn

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Adaptive fault‐tolerant control for feedback linearizable systems with an aircraft application

Gao

Wang

2014

Intl J Robust & Nonlinear

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SummaryThis paper investigates fault‐tolerant control (FTC) for feedback linearizable systems (FLSs) and its applications. The dynamic effects caused by the actuator faults on the feedback linearized model are firstly analyzed, which reveals that under actuator faults, the control input in the linearized model is affected by uncertain terms. In the framework of model reference control, the first FTC strategy is proposed as a robust controller, which achieves asymptotic tracking control of the FLS under actuator faults. A disadvantage of this strategy is that it relies on explicit information about several parameters in the actuator faults. This requirement is later relaxed by combining the robust FTC strategy with an adaptive technique to generate the adaptive FTC law, which is then improved to alleviate possible chattering of the actuator and estimation drifting of the adaptive parameter. Finally, the proposed FTC strategies are evaluated by reference command tracking control of a pendulum and an air‐breathing hypersonic vehicle under actuator faults. Simulation results demonstrate good tracking performance, which confirms effectiveness of the proposed strategies. Copyright © 2014 John Wiley & Sons, Ltd.

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Extended Jacobian inverse kinematics algorithms for mobile manipulators

Tchoń

Jakubiak

2002

J. Robotic Syst.

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We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.

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A path space approach to nonholonomic motion planning in the presence of obstacles

Cited by 106 publications

References 25 publications

The planning of optimal motions of non-holonomic systems

The planning of optimal motions of non-holonomic systems

Adaptive fault‐tolerant control for feedback linearizable systems with an aircraft application

Extended Jacobian inverse kinematics algorithms for mobile manipulators

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