Modern trajectory optimization based approaches to motion planning are fast, easy to implement, and effective on a wide range of robotics tasks. However, trajectory optimization algorithms have parameters that are typically set in advance (and rarely discussed in detail). Setting these parameters properly can have a significant impact on the practical performance of the algorithm, sometimes making the difference between finding a feasible plan or failing at the task entirely. We propose a method for leveraging past experience to learn how to automatically adapt the parameters of Gaussian Process Motion Planning (GPMP) algorithms. Specifically, we propose a differentiable extension to the GPMP2 algorithm, so that it can be trained end-to-end from data. We perform several experiments that validate our algorithm and illustrate the benefits of our proposed learning-based approach to motion planning.
Recent work in structured learning techniques offer avenues towards contending with these challenges. Several methods have focused on incorporating optimization within neural network architectures. For example, @cite_8 implicitly learns to perform nonlinear least squares optimization by learning an RNN that predicts its update steps, @cite_16 learns to perform gradient descent, and @cite_18 utilizes a ODE solver within its network. Other methods like @cite_6 learn a sequential quadratic program as a layer in its network, which was later extended to solve model predictive control @cite_10 . @cite_9 learns structured dynamics models for reactive visuomotor control. Taking inspiration from this body of work, in this paper we present a differentiable inference-based motion planning technique that through its structure allows us to combine the strengths of both traditional model-based methods and modern learning methods, while mitigating their respective weaknesses.
@cite_18 @cite_8 @cite_9 @cite_6 @cite_16 @cite_10
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Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate real-time control of biological brain. Due to incomplete neural and anatomical data, traditional neural network training methods fail to model the sensory-motor systems. Here we introduce a novel modeling method based on stochastic optimal control framework which is well suited for this purpose. Our controller is implemented with a recurrent neural network (RNN) whose goal is approximating the optimal global control law for the given plant and cost function. We employ a risk-sensitive objective function proposed by Jacobson (1973) for robustness of controller. For maximum optimization efficiency, we introduce a step response sampling method, which minimizes complexity of the optimization problem. We use conjugate gradient descent method for optimization, and gradient is calculated via Pontryagins maximum principle. In the end, we obtain highly stable and robust RNN controllers that can generate infinite varieties of attractor dynamics of the plant, which are proposed as building blocks of movement generation. We show two such examples, a point attractor based and a limit-cycle based dynamics. Feedforward multilayer networks trained by supervised learning have recently demonstrated state of the art performance on image labeling problems such as boundary prediction and scene parsing. As even very low error rates can limit practical usage of such systems, methods that perform closer to human accuracy remain desirable. In this work, we propose a new type of network with the following properties that address what we hypothesize to be limiting aspects of existing methods: (1) a wide' structure with thousands of features, (2) a large field of view, (3) recursive iterations that exploit statistical dependencies in label space, and (4) a parallelizable architecture that can be trained in a fraction of the time compared to benchmark multilayer convolutional networks. For the specific image labeling problem of boundary prediction, we also introduce a novel example weighting algorithm that improves segmentation accuracy. Experiments in the challenging domain of connectomic reconstruction of neural circuity from 3d electron microscopy data show that these "Deep And Wide Multiscale Recursive" (DAWMR) networks lead to new levels of image labeling performance. The highest performing architecture has twelve layers, interwoven supervised and unsupervised stages, and uses an input field of view of 157,464 voxels ( @math ) to make a prediction at each image location. We present an associated open source software package that enables the simple and flexible creation of DAWMR networks. Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to constrain the incoming weights of each neuron to be unit-norm, which is formulated as an optimization problem over Oblique manifold. A simple yet efficient method referred to as projection based weight normalization (PBWN) is also developed to solve this problem. PBWN executes standard gradient updates, followed by projecting the updated weight back to Oblique manifold. This proposed method has the property of regularization and collaborates well with the commonly used batch normalization technique. We conduct comprehensive experiments on several widely-used image datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet for supervised learning over the state-of-the-art convolutional neural networks, such as Inception, VGG and residual networks. The results show that our method is able to improve the performance of DNNs with different architectures consistently. We also apply our method to Ladder network for semi-supervised learning on permutation invariant MNIST dataset, and our method outperforms the state-of-the-art methods: we obtain test errors as 2.52 , 1.06 , and 0.91 with only 20, 50, and 100 labeled samples, respectively. In this paper, we address the problem of incrementally optimizing constraint networks for maximum likelihood map learning. Our approach allows a robot to efficiently compute configurations of the network with small errors while the robot moves through the environment. We apply a variant of stochastic gradient descent and use a tree-based parameterization of the nodes in the network. By integrating adaptive learning rates in the parameterization of the network, our algorithm can use previously computed solutions to determine the result of the next optimization run. Additionally, our approach updates only the parts of the network which are affected by the newly incorporated measurements and starts the optimization approach only if the new data reveals inconsistencies with the network constructed so far. These improvements yield an efficient solution for this class of online optimization problems. Our approach has been implemented and tested on simulated and on real data. We present comparisons to recently proposed online and offline methods that address the problem of optimizing constraint network. Experiments illustrate that our approach converges faster to a network configuration with small errors than the previous approaches.