8 research outputs found
Time-optimal Coordination of Mobile Robots along Specified Paths
In this paper, we address the problem of time-optimal coordination of mobile
robots under kinodynamic constraints along specified paths. We propose a novel
approach based on time discretization that leads to a mixed-integer linear
programming (MILP) formulation. This problem can be solved using
general-purpose MILP solvers in a reasonable time, resulting in a
resolution-optimal solution. Moreover, unlike previous work found in the
literature, our formulation allows an exact linear modeling (up to the
discretization resolution) of second-order dynamic constraints. Extensive
simulations are performed to demonstrate the effectiveness of our approach.Comment: Published in 2016 IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS
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
Multi Vehicle Trajectory Planning On Road Networks
When multiple autonomous vehicles work in a shared space, such as in a surface mine or warehouse, they often travel along specified paths through a static road network. Although these vehicles’ actions and performance are coupled, their motion is often planned myopically or omits cooperation beyond avoiding collisions reactively. More desirable solutions could be achieved by coordinating and planning actions ahead of time.
To make multi-vehicle systems more productive and efficient, the thesis introduces planning methods that can optimise for travel time, energy consumption, and trajectory smoothness. Vehicle motion is coordinated by using motion models that combine all trajectories, and avoid collisions. Mathematical programming is then used to find optimised solutions. The proposed methods are shown to significantly reduce solution costs compared to an approach based on common driving practices.
As the number of vehicles and interactions between them increases, the number of solutions grows exponentially, making finding a solution computationally challenging. A major aim here was to find high quality solutions within practical computation times. To achieve this, techniques were developed that exploit the structure of the problems. This includes a heuristic algorithm that scales better with problem size, and is combined with the mathematical programming techniques to reduce their complexity. These were found to significantly reduce computation times, trading off marginal solution quality