21 research outputs found
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
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
Model Predictive Control for Autonomous Driving Based on Time Scaled Collision Cone
In this paper, we present a Model Predictive Control (MPC) framework based on
path velocity decomposition paradigm for autonomous driving. The optimization
underlying the MPC has a two layer structure wherein first, an appropriate path
is computed for the vehicle followed by the computation of optimal forward
velocity along it. The very nature of the proposed path velocity decomposition
allows for seamless compatibility between the two layers of the optimization. A
key feature of the proposed work is that it offloads most of the responsibility
of collision avoidance to velocity optimization layer for which computationally
efficient formulations can be derived. In particular, we extend our previously
developed concept of time scaled collision cone (TSCC) constraints and
formulate the forward velocity optimization layer as a convex quadratic
programming problem. We perform validation on autonomous driving scenarios
wherein proposed MPC repeatedly solves both the optimization layers in receding
horizon manner to compute lane change, overtaking and merging maneuvers among
multiple dynamic obstacles.Comment: 6 page
A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in
robotics and has a wide range of applications. There are two main families of
methods to address TOPP: Numerical Integration (NI) and Convex Optimization
(CO). NI-based methods are fast but difficult to implement and suffer from
robustness issues, while CO-based approaches are more robust but at the same
time significantly slower. Here we propose a new approach to TOPP based on
Reachability Analysis (RA). The key insight is to recursively compute reachable
and controllable sets at discretized positions on the path by solving small
Linear Programs (LPs). The resulting algorithm is faster than NI-based methods
and as robust as CO-based ones (100% success rate), as confirmed by extensive
numerical evaluations. Moreover, the proposed approach offers unique additional
benefits: Admissible Velocity Propagation and robustness to parametric
uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure
A randomized kinodynamic planner for closed-chain robotic systems
Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin
Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots
Path-velocity decomposition is an intuitive yet powerful approach to address
the complexity of kinodynamic motion planning. The difficult trajectory
planning problem is solved in two separate, simpler, steps: first, find a path
in the configuration space that satisfies the geometric constraints (path
planning), and second, find a time-parameterization of that path satisfying the
kinodynamic constraints. A fundamental requirement is that the path found in
the first step should be time-parameterizable. Most existing works fulfill this
requirement by enforcing quasi-static constraints in the path planning step,
resulting in an important loss in completeness. We propose a method that
enables path-velocity decomposition to discover truly dynamic motions, i.e.
motions that are not quasi-statically executable. At the heart of the proposed
method is a new algorithm -- Admissible Velocity Propagation -- which, given a
path and an interval of reachable velocities at the beginning of that path,
computes exactly and efficiently the interval of all the velocities the system
can reach after traversing the path while respecting the system kinodynamic
constraints. Combining this algorithm with usual sampling-based planners then
gives rise to a family of new trajectory planners that can appropriately handle
kinodynamic constraints while retaining the advantages associated with
path-velocity decomposition. We demonstrate the efficiency of the proposed
method on some difficult kinodynamic planning problems, where, in particular,
quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure