32 research outputs found
Time-Optimal Path Tracking via Reachability Analysis
Given a geometric path, the Time-Optimal Path Tracking problem consists in
finding the control strategy to traverse the path time-optimally while
regulating tracking errors. A simple yet effective approach to this problem is
to decompose the controller into two components: (i)~a path controller, which
modulates the parameterization of the desired path in an online manner,
yielding a reference trajectory; and (ii)~a tracking controller, which takes
the reference trajectory and outputs joint torques for tracking. However, there
is one major difficulty: the path controller might not find any feasible
reference trajectory that can be tracked by the tracking controller because of
torque bounds. In turn, this results in degraded tracking performances. Here,
we propose a new path controller that is guaranteed to find feasible reference
trajectories by accounting for possible future perturbations. The main
technical tool underlying the proposed controller is Reachability Analysis, a
new method for analyzing path parameterization problems. Simulations show that
the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201
Critically fast pick-and-place with suction cups
Fast robotics pick-and-place with suction cups is a crucial component in the
current development of automation in logistics (factory lines, e-commerce,
etc.). By "critically fast" we mean the fastest possible movement for
transporting an object such that it does not slip or fall from the suction cup.
The main difficulties are: (i) handling the contact between the suction cup and
the object, which fundamentally involves kinodynamic constraints; and (ii)
doing so at a low computational cost, typically a few hundreds of milliseconds.
To address these difficulties, we propose (a) a model for suction cup contacts,
(b) a procedure to identify the contact stability constraint based on that
model, and (c) a pipeline to parameterize, in a time-optimal manner, arbitrary
geometric paths under the identified contact stability constraint. We
experimentally validate the proposed pipeline on a physical robot system: the
cycle time for a typical pick-and-place task was less than 5 seconds, planning
and execution times included. The full pipeline is released as open-source for
the robotics community.Comment: 7 pages, 5 figure
Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm
Time Optimal Path Parametrization is the problem of minimizing the time
interval during which an actuation constrained agent can traverse a given path.
Recently, an efficient linear-time algorithm for solving this problem was
proposed. However, its optimality was proved for only a strict subclass of
problems solved optimally by more computationally intensive approaches based on
convex programming. In this paper, we prove that the same linear-time algorithm
is asymptotically optimal for all problems solved optimally by convex
optimization approaches. We also characterize the optimum of the Time Optimal
Path Parametrization Problem, which may be of independent interest
Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas
Humanoid robots locomote by making and breaking contacts with their
environment. A crucial problem is therefore to find precise criteria for a
given contact to remain stable or to break. For rigid surface contacts, the
most general criterion is the Contact Wrench Condition (CWC). To check whether
a motion satisfies the CWC, existing approaches take into account a large
number of individual contact forces (for instance, one at each vertex of the
support polygon), which is computationally costly and prevents the use of
efficient inverse-dynamics methods. Here we argue that the CWC can be
explicitly computed without reference to individual contact forces, and give
closed-form formulae in the case of rectangular surfaces -- which is of
practical importance. It turns out that these formulae simply and naturally
express three conditions: (i) Coulomb friction on the resultant force, (ii) ZMP
inside the support area, and (iii) bounds on the yaw torque. Conditions (i) and
(ii) are already known, but condition (iii) is, to the best of our knowledge,
novel. It is also of particular interest for biped locomotion, where undesired
foot yaw rotations are a known issue. We also show that our formulae yield
simpler and faster computations than existing approaches for humanoid motions
in single support, and demonstrate their consistency in the OpenHRP simulator.Comment: 14 pages, 4 figure
Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level
The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions