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A technique is developed for vehicle navigation and control in the presence of obstacles. A potential function was devised that peaks at the surface of obstacles and has its minimum at the proper vehicle destination. This function is computed using a systolic array and is guaranteed not to have local minima. A feedfoward neural network is then used to control the steering of the vehicle using local potential field information. In this case, the vehicle is a trailer truck backing up. Previous work has demonstrated the capability of a neural network to control steering of such a trailer truck backing to a loading platform, but without obstacles. Now, the neural network was able to learn to navigate a trailer truck around obstacles while backing toward its destination. The network is trained in an obstacle free space to follow the negative gradient of the field, after which the network is able to control and navigate the truck to its target destination in a space of obstacles which may be stationary or movable.

Sin and sorrow are twin sisters. They were born the same day. They have grown up together. It is as idle to say that there is no misery as to assert that there is no wickedness in the world. Some men seem to be uniformly prosperous. They appear to have but few trials. They have more than heart can wish. They are receiving their good things in this life. They are the abhorred of the Lord. Their eternity will be rueful. Yet even they have their seasons of weariness. And the mass of men have many and palpable sorrows. This is always true of the godly in this life: "Many are the afflictions of the righteous." "Whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth." The tears of God's people often flow, day and night. Waters of a full cup are wrung out to them. Oh, the weariness of good men! It has many causes. - Summary by William S. Plumer