We present a robust motion planning algorithm for a holonomic mobile robot that incorporates the risk of collisions directly in the cost function. This deterministic algorithm uses analytic predictions of the path-following error statistics to quickly calculate the collision risk. The A* search algorithm is used to find motion plans that optimally balance the plan duration with the collision risk, and these plans have a higher probability of success than plans that do not consider the collision risk. We present experimental results for an autonomous marine vehicle.
Abstract-Path planning algorithms that incorporate risk and uncertainty need to be able to predict the evolution of pathfollowing error statistics for each candidate plan. We present an analytic method to predict the evolving error statistics of a holonomic vehicle following a reference trajectory in a planar environment. This method is faster than integrating the plant through time or performing a Monte Carlo simulation. It can be applied to systems with external Gaussian disturbances, and it can be extended to handle plant uncertainty through numerical quadrature techniques.
For a mobile robot that performs online model learning, the learning rate is a function of the robot's trajectory. The tracking errors that arise when the robot executes a motion plan depend on how well the robot has learned its own model. Therefore a planner that seeks to minimize collisions with obstacles will choose plans that decrease modeling errors if it can predict the learning rate for each plan. In this paper we present an integrated planning and learning algorithm for a simple mobile robot that finds safe, efficient plans through a grid world to a goal point using a standard optimal planner, A*. Simulation results show that with this algorithm the robot practices maneuvers in the open regions of the configuration space, if necessary, before entering the constrained regions of the space. The robot performs mission-specific learning, acquiring only the information it needs to complete the task safely.
First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times, for a class of linear continuous, time-varying systems. In several examples we show that the algorithm is both accurate and timeefficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.
Nomenclature x(t)State vector.
y(t)System output, scalar.A(t), G(t), C System matrices.
w(t)Unit Wiener noise process, vector.Lower and upper boundaries, scalar.
Σ Σ Σ(t)State covariance matrix.Σ y (t) Output covariance, scalar.P a (t) Probability of no collision, scalar.P hit (t) Collision probability, 1 − P a (t), scalar.
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