33,667 research outputs found
Chance-Constrained Optimal Path Planning With Obstacles
Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. For robust execution, we must take into account uncertainty, which arises due to uncertain localization, modeling errors, and disturbances. Prior work handled the case of set-bounded uncertainty. We present here a chance-constrained approach, which uses instead a probabilistic representation of uncertainty. The new approach plans the future probabilistic distribution of the vehicle state so that the probability of failure is below a specified threshold. Failure occurs when the vehicle collides with an obstacle or leaves an operator-specified region. The key idea behind the approach is to use bounds on the probability of collision to show that, for linear-Gaussian systems, we can approximate the nonconvex chance-constrained optimization problem as a disjunctive convex program. This can be solved to global optimality using branch-and-bound techniques. In order to improve computation time, we introduce a customized solution method that returns almost-optimal solutions along with a hard bound on the level of suboptimality. We present an empirical validation with an aircraft obstacle avoidance example.National Science Foundation (U.S.) (Grant IIS-1017992)Boeing Company (Grant MIT-BA-GTA-1
Fast Second-order Cone Programming for Safe Mission Planning
This paper considers the problem of safe mission planning of dynamic systems
operating under uncertain environments. Much of the prior work on achieving
robust and safe control requires solving second-order cone programs (SOCP).
Unfortunately, existing general purpose SOCP methods are often infeasible for
real-time robotic tasks due to high memory and computational requirements
imposed by existing general optimization methods. The key contribution of this
paper is a fast and memory-efficient algorithm for SOCP that would enable
robust and safe mission planning on-board robots in real-time. Our algorithm
does not have any external dependency, can efficiently utilize warm start
provided in safe planning settings, and in fact leads to significant speed up
over standard optimization packages (like SDPT3) for even standard SOCP
problems. For example, for a standard quadrotor problem, our method leads to
speedup of 1000x over SDPT3 without any deterioration in the solution quality.
Our method is based on two insights: a) SOCPs can be interpreted as
optimizing a function over a polytope with infinite sides, b) a linear function
can be efficiently optimized over this polytope. We combine the above
observations with a novel utilization of Wolfe's algorithm to obtain an
efficient optimization method that can be easily implemented on small embedded
devices. In addition to the above mentioned algorithm, we also design a
two-level sensing method based on Gaussian Process for complex obstacles with
non-linear boundaries such as a cylinder
Reliable autonomous vehicle control - a chance constrained stochastic MPC approach
In recent years, there is a growing interest in the development of systems capable of performing
tasks with a high level of autonomy without human supervision. This kind of systems are known as
autonomous systems and have been studied in many industrial applications such as automotive,
aerospace and industries. Autonomous vehicle have gained a lot of interest in recent years and have
been considered as a viable solution to minimize the number of road accidents. Due to the
complexity of dynamic calculation and the physical restrictions in autonomous vehicle, for example,
deterministic model predictive control is an attractive control technique to solve the problem of
path planning and obstacle avoidance. However, an autonomous vehicle should be capable of driving
adaptively facing deterministic and stochastic events on the road. Therefore, control design for
the safe, reliable and autonomous driving should consider vehicle model uncertainty as well
uncertain external influences. The stochastic model predictive control scheme provides the
most convenient scheme for the control of autonomous vehicles on moving horizons, where chance
constraints are to be used to guarantee the reliable fulfillment of trajectory constraints and
safety against static and random obstacles. To solve this kind of problems is known as chance
constrained model predictive control. Thus, requires the solution of a chance constrained
optimization on moving horizon. According to the literature, the major challenge for solving chance
constrained optimization is to calculate the value of probability. As a result, approximation
methods have been proposed for solving this task.
In the present thesis, the chance constrained optimization for the autonomous vehicle is solved
through approximation method, where the probability constraint is approximated by using a smooth
parametric function. This methodology presents two approaches that allow the solution of chance
constrained optimization problems in inner approximation and outer approximation. The aim of this
approximation methods is to reformulate the chance constrained optimizations problems as a sequence
of nonlinear programs. Finally, three case studies of autonomous vehicle for tracking and obstacle
avoidance are presented in this work, in which three levels probability of reliability are
considered
for the optimal solution.Tesi
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