Robot navigation functions on manifolds with boundary

Koditschek, Daniel E.; Rimon, Elon

doi:10.1016/0196-8858(90)90017-s

Cited by 496 publications

(552 citation statements)

References 8 publications

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“…Our potential shaping approach is inspired by [12] and [28]. Other relevant work involving energy methods in control and stabilization includes [1], [3], [18], [26], [33], [34], [37], [38], and [41]. In [6], we relate the potential shaping approach here to that of [24], [25], and [40].…”

Section: B History and Related Literaturementioning

confidence: 99%

“…Therefore, there is a function for an open subset in such that (23) We introduce a new coordinate chart for as follows: (24) This coordinate change induces the following new local coordinates for : (25) Notice that this change of coordinates fixes the equilibrium , i.e., . In the new coordinates, the PDE (16) becomes (26) Assume that we have a solution to this PDE. Then, the mixed partials of should be equal, i.e.,…”

Section: A Notationmentioning

confidence: 99%

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Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Bloch

Chang

Leonard

et al. 2001

IEEE Trans. Automat. Contr.

298

232

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Abstract-We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.

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Section: B History and Related Literaturementioning

confidence: 99%

Section: A Notationmentioning

confidence: 99%

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Bloch

Chang

Leonard

et al. 2001

IEEE Trans. Automat. Contr.

298

232

View full text Add to dashboard Cite

show abstract

“…More precisely, let V : F → R be an artificial potential function that is i) twice differentiable on F, ii) polar at x * , i.e., has a unique local minimum at x * , iii) is a Morse function [16], i.e., has no degenerate critical points, iv) is admissible [16] on F, i.e., takes its maximum value uniformly on the boundary ∂F of F. Such a potential function is referred to as a navigation function [6], [17], because its negated gradient fielḋ…”

Section: A Smooth Extensions Of Gradient Dynamics Via Total Energymentioning

confidence: 99%

Smooth extensions of feedback motion planners via reference governors

Arslan

Koditschek

2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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In robotics, it is often practically and theoretically convenient to design motion planners for approximate loworder (e.g., position-or velocity-controlled) robot models first, and then adapt such reference planners to more accurate high-order (e.g., force/torque-controlled) robot models. In this paper, we introduce a novel provably correct approach to extend the applicability of low-order feedback motion planners to high-order robot models, while retaining stability and collision avoidance properties, as well as enforcing additional constraints that are specific to the high-order models. Our smooth extension framework leverages the idea of reference governors to separate the issues of stability and constraint satisfaction, affording a bidirectionally coupled robot-governor system where the robot ensures stability with respect to the governor and the governor enforces state (e.g., collision avoidance) and control (e.g., actuator limits) constraints. We demonstrate example applications of our framework for augmenting path planners and vector field planners to the second-order robot dynamics.Keywords smooth extensions; command governors; reference governors; collision avoidance;robot dynamics;stability;collision avoidance;constraint satisfaction;feedback motion planners;path planners;reference governors;robot models;robot-governor system;robotics;second-order robot dynamics;smooth extensions;stability;vector field planners;Asymptotic stability;Collision avoidance;Computational modeling;Dynamics;Navigation;Robots;Stability analysis Disciplines Computer Engineering | Controls and Control Theory | Electrical and Computer Engineering | Engineering | RoboticsThis conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/790 Smooth Extensions of Feedback Motion Planners via Reference GovernorsOmur Arslan and Daniel E. KoditschekAbstract-In robotics, it is often practically and theoretically convenient to design motion planners for approximate loworder (e.g., position-or velocity-controlled) robot models first, and then adapt such reference planners to more accurate highorder (e.g., force/torque-controlled) robot models. In this paper, we introduce a novel provably correct approach to extend the applicability of low-order feedback motion planners to high-order robot models, while retaining stability and collision avoidance properties, as well as enforcing additional constraints that are specific to the high-order models. Our smooth extension framework leverages the idea of reference governors to separate the issues of stability and constraint satisfaction, affording a bidirectionally coupled robot-governor system where the robot ensures stability with respect to the governor and the governor enforces state (e.g., collision avoidance) and control (e.g., actuator limits) constraints. We demonstrate example applications of our framework for augmenting path planners and vector field planners to the second-order robot dynamics.

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“…In 31,32,42,46], micro-actuator arrays present us with the ability t o explicitly program the applied force at every point in a vector eld. 3 Several groups have described e orts to apply MEMS actuators to positioning, inspection, and assembly tasks with small parts 3, 14, 27, 33, 40, for example].…”

Section: A Previous Workmentioning

confidence: 99%

Part orientation with one or two stable equilibria using programmable force fields

Böhringer

Donald

Kavraki

et al. 2000

IEEE Trans. Robot. Automat.

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Programmable force elds are an abstraction to represent a new class of devices for distributed, nonprehensile manipulation for applications in parts feeding, sorting, positioning, and assembly. Unlike r o b o t grippers, conveyor belts, or vibratory bowl feeders, these devices generate force vector elds in which the parts move u n til they may reach a stable equilibrium pose.Recent research in the theory of programmable force elds has yielded open-loop strategies to uniquely position, orient, and sort parts. These strategies typically consist of several elds that have to be employed in sequence to achieve a desired nal pose. The length of the sequence depends on the complexity of the part.In this paper, we show that unique part poses can be achieved with just one eld. First, we exhibit a single eld that positions and orients any part (with the exception of certain symmetric parts) into two stable equilibrium poses. Then we show that for any part there exists a eld in which the part reaches a unique stable equilibrium pose (again with the exception of symmetric parts). Besides giving an optimal upper bound for unique parts positioning and orientation, our work gives further evidence that programmable force elds are a powerful tool for parts manipulation.Our second result also leads to the design of \universal parts feeders", proving an earlier conjecture about their existence. We argue that universal parts feeders are relatively easy to build, and we report on extensive s i m ulation results which indicate that these devices may w ork very well in practice. We believe that the results in this paper could be the basis for a new generation of e cient, open-loop, parallel parts feeders.

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Robot navigation functions on manifolds with boundary

Cited by 496 publications

References 8 publications

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Smooth extensions of feedback motion planners via reference governors

Part orientation with one or two stable equilibria using programmable force fields

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