S n, the robot has redundant degrees-of-freedom (dof's). In general, control objectives such as the positioning and orienting of the endeffector are specified with respect to task space coordinates; however, the manipulator is typica1ly controlled only in the configuration space.

Trajectory generation finds interesting applications in the field of robotics, automation, filtering, or time series prediction. Neural networks, with their ability to learn from examples, have been proposed very early on for solving nonlinear control problems adaptively. Several neural net architectures have been proposed for trajectory generation, most notably recurrent networks, either with discrete time and externalloops (Jordan, 1986), or with continuous time (Pearlmutter, 1988). Aside from being recurrent, these networks are not specifically tailored for trajectory generation. It has been shown that specific architectures, such as the Time Delay Neural Networks (Lang and Hinton, 1988), or convolutional networks in general, are better than fully connected networks at recognizing time sequences such as speech (Waibel et al., 1989), or pen trajectories (Guyon et al., 1991). We show that special architectures can also be devised for trajectory generation, with dramatic performance improvement.

A large class of motor control tasks requires that on each cycle the controller is told its current state and must choose an action to achieve a specified, state-dependent, goal behaviour. This paper argues that the optimization of learning rate, the number of experimental control decisions before adequate performance is obtained, and robustness is of prime importance-if necessary at the expense of computation per control cycle and memory requirement. This is motivated by the observation that a robot which requires two thousand learning steps to achieve adequate performance, or a robot which occasionally gets stuck while learning, will always be undesirable, whereas moderate computational expense can be accommodated by increasingly powerful computer hardware. It is not unreasonable to assume the existence of inexpensive 100 Mflop controllers within a few years and so even processes with control cycles in the low tens of milliseconds will have millions of machine instructions in which to make their decisions. This paper outlines a learning control scheme which aims to make effective use of such computational power. 1 MEMORY BASED LEARNING Memory-based learning is an approach applicable to both classification and function learning in which all experiences presented to the learning box are explicitly remembered. The memory, Mem, is a set of input-output pairs, Mem {(Xl, YI), (X21 Y2),..., (Xb Yk)}.

A method for transforming performance evaluation signals distal both in space and time into proximal signals usable by supervised learning algorithms, presented in [Jordan & Jacobs 90], is examined. A simple observation concerning differentiation through models trained with redundant inputs (as one of their networks is) explains a weakness in the original architecture and suggests a modification: an internal world model that encodes action-space exploration and, crucially, cancels input redundancy to the forward model is added. Learning time on an example task, cartpole balancing, is thereby reduced about 50 to 100 times. 1 INTRODUCTION In many learning control problems, the evaluation used to modify (and thus improve) control may not be available in terms of the controller's output: instead, it may be in terms of a spatial transformation of the controller's output variables (in which case we shall term it as being "distal in space"), or it may be available only several time steps into the future (termed as being "distal in time"). For example, control of a robot arm may be exerted in terms of joint angles, while evaluation may be in terms of the endpoint cartesian coordinates; furthermore, we may only wish to evaluate the endpoint coordinates reached after a certain period of time: the co- ·Current address: Computation and Neural Systems Program, California Institute of Technology, Pasadena CA.

We apply this method to the task of controlling the outflow and temperature of a water tank, producing statistically-significant gains in accuracy over both a standard neural network approach and a non-learning PID controller. Furthermore, using the PID knowledge to initialize the weights of the network produces statistically less variation in testset accuracy when compared to networks initialized with small random numbers.

We present two neural network controller learning schemes based on feedbackerror-learning and modular architecture for recognition and control of multiple manipulated objects. In the first scheme, a Gating Network is trained to acquire object-specific representations for recognition of a number of objects (or sets of objects). In the second scheme, an Estimation Network is trained to acquire function-specific, rather than object-specific, representations which directly estimate physical parameters. Both recognition networks are trained to identify manipulated objects using somatic and/or visual information. After learning, appropriate motor commands for manipulation of each object are issued by the control networks.

Many real-valued connectionist approaches to learning control realize exploration by randomness in action selection. This might be disadvantageous when costs are assigned to "negative experiences". The basic idea presented in this paper is to make an agent explore unknown regions in a more directed manner. This is achieved by a so-called competence map, which is trained to predict the controller's accuracy, and is used for guiding exploration. Based on this, a bistable system enables smoothly switching attention between two behaviors - exploration and exploitation - depending on expected costs and knowledge gain. The appropriateness of this method is demonstrated by a simple robot navigation task.

Intrator (1990) proposed a feature extraction method that is related to recent statistical theory (Huber, 1985; Friedman, 1987), and is based on a biologically motivated model of neuronal plasticity (Bienenstock et al., 1982). This method has been recently applied to feature extraction in the context of recognizing 3D objects from single 2D views (Intrator and Gold, 1991). Here we describe experiments designed to analyze the nature of the extracted features, and their relevance to the theory and psychophysics of object recognition. 1 Introduction Results of recent computational studies of visual recognition (e.g., Poggio and Edelman, 1990) indicate that the problem of recognition of 3D objects can be effectively reformulated in terms of standard pattern classification theory. According to this approach, an object is represented by a few of its 2D views, encoded as clusters in multidimentional space. Recognition of a novel view is then carried out by interpo-460 3D Object Recognition Using Unsupervised Feature Extraction 461 lating among the stored views in the representation space.

Visual object recognition involves the identification of images of 3-D objects seen from arbitrary viewpoints. We suggest an approach to object recognition in which a view is represented as a collection of points given by their location in the image. An object is modeled by a set of 2-D views together with the correspondence between the views. We show that any novel view of the object can be expressed as a linear combination of the stored views. Consequently, we build a linear operator that distinguishes between views of a specific object and views of other objects.

Despite the fact that complex visual scenes contain multiple, overlapping objects, people perform object recognition with ease and accuracy. One operation that facilitates recognition is an early segmentation process in which features of objects are grouped and labeled according to which object they belong. Current computational systems that perform this operation are based on predefined grouping heuristics.