Complete maps of molecular‐loop conformational spaces

Many situations in Robotics require the analysis of the motions of complex multibody systems. These are sets of articulated bodies arising in a variety of devices, including parallel manipulators, multifingered hands, or reconfigurable mechanisms, but they appear in other domains too, as mechanical models of molecular compounds or nanostructures. Closed kinematic chains arise frequently in such systems, either due to their morphology, or to geometric or contact constraints to fulfill during operation, giving rise to configuration spaces of an intricate structure. Despite appearing very often in practice, there is a lack of general software tools to analyze and represent such configuration spaces. Existing packages are either oriented to open chain systems, or to specific robot types, which hinders the analysis and development of innovative manipulators. This paper describes the CUIK suite, a software toolbox for the kinematic analysis of general multibody systems. The implemented tools can isolate the valid configurations, determine the motion range of the whole multibody system or of some of its parts, detect singular configurations leading to control or dexterity issues, or find collision-and singularity-free paths between configurations. The toolbox has applications in robot design and programming, and it is the result of several years of research and development within the Kinematics and Robot Design group at IRI, Barcelona. It is available under GPLv3 license from

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“…7. This process would require costly computations using single-CPU machines or alternative approaches [22]. Figure 6.…”

Section: Branch-and-prune Methodsmentioning

confidence: 99%

The CUIK Suite: Analyzing the Motion Closed-Chain Multibody Systems

Porta

Ros

Bohigas

et al. 2014

IEEE Robot. Automat. Mag.

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“…The example in Fig. 3 is simple, but the tools have proved successful in analysing the C-spaces of general 6R robots and Stewart platforms [16], multiloop molecules [17], robot hands with contact constraints [20], or complex multi-loop linkages like the one in Fig. 3.…”

Section: Branch-and-prune Methodsmentioning

confidence: 99%

An Open-Source Toolbox for Motion Analysis of Closed-Chain Mechanisms

Porta

Ros

Bohigas

et al. 2013

Computational Kinematics

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Many situations in Robotics require an effective analysis of the motions of a closed-chain mechanism. Despite appearing very often in practice (e.g. in parallel manipulators, reconfigurable robots, or molecular compounds), there is a lack of general tools to effectively analyze the complex configuration spaces of such systems. This paper describes the CUIK suite, an open-source toolbox for motion analysis of general closed-chain mechanisms. The package can determine the motion range of the whole mechanism or of some of its parts, detect singular configurations leading to control or dexterity issues, or find collision-and singularity-free paths between given configurations. The toolbox is the result of several years of research and development within the Kinematics and Robot Design group at IRI, Barcelona, and is available under GPLv3 license from http://www.iri.upc.edu/cuik.

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“…For strictly constrained problems, we present a systematic method based on higher-dimensional continuation. This technique continues the research line initiated in [46] which aims at developing tools to isolate the full conformational space of molecular loops. However, the method presented in [46] is complete, while the method introduded here defines an atlas of the connected component of the conformational space reachable from a given point.…”

Section: Related Workmentioning

confidence: 99%

“…This technique continues the research line initiated in [46] which aims at developing tools to isolate the full conformational space of molecular loops. However, the method presented in [46] is complete, while the method introduded here defines an atlas of the connected component of the conformational space reachable from a given point. This sacrifice in completeness, though, results in a significant increment in computational efficiency.…”

Section: Related Workmentioning

confidence: 99%

“…Although these techniques can be iterated, they are designed to obtain one solution at a time. Numerical methods able to isolate the whole conformational space and that are not affected by singularities also exist [46]. Finally, problems with more degrees of freedom can also be addressed with local perturbation techniques [58,35], with approaches where some of the variables are sampled and the rest is solved via inverse kinematics [15,14] or combining inverse kinematics, fragment assembly, and local optimization methods [26,36].…”

Section: Related Workmentioning

confidence: 99%

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Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

Porta

Jaillet

2012

J Comput Chem

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The conformational space of a flexible molecular loop includes the set of conformations fulfilling the geometric loop-closure constraints and its energy landscape can be seen as a scalar field defined on this implicit set. Higher-dimensional continuation tools, recently developed in Dynamical Systems and also applied to Robotics, provide efficient algorithms to trace out implicitly defined sets. This paper describes these tools and applies them to obtain full descriptions of the energy landscapes of short molecular loops that, otherwise, can only be partially explored, mainly via sampling. Moreover, to deal with larger loops, this paper exploits the higher-dimensional continuation tools to find local minima and minimum energy transition paths between them, without deviating from the loop-closure constraints. The proposed techniques are applied to previously studied molecules revealing the intricate structure of their energy landscapes. This paper introduces the use of higher-dimensional continuation tools to explore the energy landscapes of the implicitly-defined conformational spaces of flexible molecular loops. These tools produce an atlas composed by coordinated charts that parametrize the conformational space. The atlas captures the structure of this space, which determines the motion of the loop and the transition paths between conformations, something that is hard to obtain using existing approaches.

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Complete maps of molecular‐loop conformational spaces

Cited by 19 publications

References 14 publications

The CUIK Suite: Analyzing the Motion Closed-Chain Multibody Systems

The CUIK Suite: Analyzing the Motion Closed-Chain Multibody Systems

An Open-Source Toolbox for Motion Analysis of Closed-Chain Mechanisms

Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

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