بحث بعنوان Workspace Computation of Planar Continuum Parallel Robots

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Workspace Computation of Planar Continuum Parallel Robots
Federico Zaccaria1;3, Edoardo Ida´1, Sebastien Briot ´ 2 and Marco Carricato1

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Abstract—Continuum parallel robots (CPRs) comprise several
flexible beams connected in parallel to an end-effector. They combine the inherent compliance of continuum robots with the high
payload capacity of parallel robots. Workspace characterization
is a crucial point in the performance evaluation of CPRs. In this
paper, we propose a methodology for the workspace evaluation
of planar continuum parallel robots (PCPRs), with focus on the
constant-orientation workspace. An explorative algorithm, based
on the iterative solution of the inverse geometrico-static problem
is proposed for the workspace computation of a generic PCPR.
Thanks to an energy-based modelling strategy, and derivative
approximation by finite differences, we are able to apply the
Kantorovich theorem to certify the existence, uniqueness, and
convergence of the solution of the inverse geometrico-static
problem at each step of the procedure. Three case studies are
shown to demonstrate the effectiveness of the proposed approach.
Index Terms—Continuum Parallel Robots, Workspace Evaluation, Kantorovich Theorem,
CONCLUSIONS
This paper presented an adaptive flooding algorithm for
the workspace computation of PCPRs. The algorithm may
identify unstable regions, singularity loci, incorporate external
loads, set maximum stress limits and joint bounds. Thanks
to an energy-based modelling strategy approximated through
finite differences for derivatives, the IGSP solution was certified in terms of existence, uniqueness, and convergence of
the solution, by verifying Kantorovich conditions during the
Newton-based problem-solving procedure. With this approach,
we certified the IGSP solution over a large percentage of the
workspace in a reduced computational time in comparison
with previous algorithms. However, with large workspaces
and/or small stepsizes, the flooding approach may require
the computation of a large number of points, which may be
not computationally efficient. Future work will be directed
on the integration of the adaptive flooding algorithm on
a workspace-guided design tool for PCPRs. Moreover, the
authors will investigate the workspace evaluation of CPRs and
the certification of the solution of the IGSP problem in the
spatial case.

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