3,188 research outputs found
On Time-optimal Trajectories for a Car-like Robot with One Trailer
In addition to the theoretical value of challenging optimal control problmes,
recent progress in autonomous vehicles mandates further research in optimal
motion planning for wheeled vehicles. Since current numerical optimal control
techniques suffer from either the curse of dimens ionality, e.g. the
Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g.
pseudospectral optimal control and max-plus methods, analytical
characterization of geodesics for wheeled vehicles becomes important not only
from a theoretical point of view but also from a prac tical one. Such an
analytical characterization provides a fast motion planning algorithm that can
be used in robust feedback loops. In this work, we use the Pontryagin Maximum
Principle to characterize extremal trajectories, i.e. candidate geodesics, for
a car-like robot with one trailer. We use time as the distance function. In
spite of partial progress, this problem has remained open in the past two
decades. Besides straight motion and turn with maximum allowed curvature, we
identify planar elastica as the third piece of motion that occurs along our
extr emals. We give a detailed characterization of such curves, a special case
of which, called \emph{merging curve}, connects maximum curvature turns to
straight line segments. The structure of extremals in our case is revealed
through analytical integration of the system and adjoint equations
Efficient Path Interpolation and Speed Profile Computation for Nonholonomic Mobile Robots
This paper studies path synthesis for nonholonomic mobile robots moving in
two-dimensional space. We first address the problem of interpolating paths
expressed as sequences of straight line segments, such as those produced by
some planning algorithms, into smooth curves that can be followed without
stopping. Our solution has the advantage of being simpler than other existing
approaches, and has a low computational cost that allows a real-time
implementation. It produces discretized paths on which curvature and variation
of curvature are bounded at all points, and preserves obstacle clearance. Then,
we consider the problem of computing a time-optimal speed profile for such
paths. We introduce an algorithm that solves this problem in linear time, and
that is able to take into account a broader class of physical constraints than
other solutions. Our contributions have been implemented and evaluated in the
framework of the Eurobot contest
A Real-Time Solver For Time-Optimal Control Of Omnidirectional Robots with Bounded Acceleration
We are interested in the problem of time-optimal control of omnidirectional
robots with bounded acceleration (TOC-ORBA). While there exist approximate
solutions for such robots, and exact solutions with unbounded acceleration,
exact solvers to the TOC-ORBA problem have remained elusive until now. In this
paper, we present a real-time solver for true time-optimal control of
omnidirectional robots with bounded acceleration. We first derive the general
parameterized form of the solution to the TOC-ORBA problem by application of
Pontryagin's maximum principle. We then frame the boundary value problem of
TOC-ORBA as an optimization problem over the parametrized control space. To
overcome local minima and poor initial guesses to the optimization problem, we
introduce a two-stage optimal control solver (TSOCS): The first stage computes
an upper bound to the total time for the TOC-ORBA problem and holds the time
constant while optimizing the parameters of the trajectory to approach the
boundary value conditions. The second stage uses the parameters found by the
first stage, and relaxes the constraint on the total time to solve for the
parameters of the complete TOC-ORBA problem. We further implement TSOCS as a
closed loop controller to overcome actuation errors on real robots in
real-time. We empirically demonstrate the effectiveness of TSOCS in simulation
and on real robots, showing that 1) it runs in real time, generating solutions
in less than 0.5ms on average; 2) it generates faster trajectories compared to
an approximate solver; and 3) it is able to solve TOC-ORBA problems with
non-zero final velocities that were previously unsolvable in real-time
Assistive trajectories for human-in-the-loop mobile robotic platforms
Autonomous and semi-autonomous smoothly interruptible trajectories are developed which are highly suitable for application in tele-operated mobile robots, operator on-board military mobile ground platforms, and other mobility assistance platforms. These trajectories will allow a navigational system to provide assistance to the operator in the loop, for purpose built robots or remotely operated platforms. This will allow the platform to function well beyond the line-of-sight of the operator, enabling remote operation inside a building, surveillance, or advanced observations whilst keeping the operator in a safe location. In addition, on-board operators can be assisted to navigate without collision when distracted, or under-fire, or when physically disabled by injury
Exercises Integrating High School Mathematics with Robot Motion Planning
This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align with Common Core State Standards for Mathematics
Efficient calibration of four wheel industrial AGVs
In this paper, we propose a novel method for extrinsic and intrinsic automatic calibration of four wheel industrial Automated Guided Vehicles (AGVs) compliant with Ackermann and Dual Drive kinematics. For each kinematic model the algorithm estimates the trajectories measured by an on-board sensor and the expected ones given the state of the wheels. The estimation exploits the model equations derived in this work which constrain calibration parameters and measurements from wheel encoders and sensor odometry. The parameter values are computed through closed-form solutions of least-square estimation. The method has been implemented on Programmable Logic Controllers and tested on industrial AGVs. The developed procedure computes the parameters in about 10−15 minutes, a significant improvement compared with one hour or more required by manual AGV calibration. Experiments with AGVs of various sizes in a warehouse have assessed the accuracy and stability of the proposed approach. The position accuracy achieved by AGVs calibrated with the proposed method is higher than the one achieved by manual calibration
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