1,154 research outputs found
Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers
Hybrid systems theory has become a powerful approach for designing feedback
controllers that achieve dynamically stable bipedal locomotion, both formally
and in practice. This paper presents an analytical framework 1) to address
multi-domain hybrid models of quadruped robots with high degrees of freedom,
and 2) to systematically design nonlinear controllers that asymptotically
stabilize periodic orbits of these sophisticated models. A family of
parameterized virtual constraint controllers is proposed for continuous-time
domains of quadruped locomotion to regulate holonomic and nonholonomic outputs.
The properties of the Poincare return map for the full-order and closed-loop
hybrid system are studied to investigate the asymptotic stabilization problem
of dynamic gaits. An iterative optimization algorithm involving linear and
bilinear matrix inequalities is then employed to choose stabilizing virtual
constraint parameters. The paper numerically evaluates the analytical results
on a simulation model of an advanced 3D quadruped robot, called GR Vision 60,
with 36 state variables and 12 control inputs. An optimal amble gait of the
robot is designed utilizing the FROST toolkit. The power of the analytical
framework is finally illustrated through designing a set of stabilizing virtual
constraint controllers with 180 controller parameters.Comment: American Control Conference 201
The Critical Radius in Sampling-based Motion Planning
We develop a new analysis of sampling-based motion planning in Euclidean
space with uniform random sampling, which significantly improves upon the
celebrated result of Karaman and Frazzoli (2011) and subsequent work.
Particularly, we prove the existence of a critical connection radius
proportional to for samples and dimensions:
Below this value the planner is guaranteed to fail (similarly shown by the
aforementioned work, ibid.). More importantly, for larger radius values the
planner is asymptotically (near-)optimal. Furthermore, our analysis yields an
explicit lower bound of on the probability of success. A
practical implication of our work is that asymptotic (near-)optimality is
achieved when each sample is connected to only neighbors. This is
in stark contrast to previous work which requires
connections, that are induced by a radius of order . Our analysis is not restricted to PRM and applies to a
variety of PRM-based planners, including RRG, FMT* and BTT. Continuum
percolation plays an important role in our proofs. Lastly, we develop similar
theory for all the aforementioned planners when constructed with deterministic
samples, which are then sparsified in a randomized fashion. We believe that
this new model, and its analysis, is interesting in its own right
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