A modular T-mode design approach for analog neural network hardware implementations

A modular transconductance-mode (T-mode) design approach is presented for analog hardware implementations of neural networks. This design approach is used to build a modular bidirectional associative memory network. The authors show that the size of the whole system can be increased by interconnecting more modular chips. It is also shown that by changing the interconnection strategy different neural network systems can be implemented, such as a Hopfield network, a winner-take-all network, a simplified ART1 network, or a constrained optimization network. Experimentally measured results from CMOS 2-μm double-metal, double-polysilicon prototypes (MOSIS) are presented

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

A General Rate Duality of the MIMO Multiple Access Channel and the MIMO Broadcast Channel

We present a general rate duality between the multiple access channel (MAC) and the broadcast channel (BC) which is applicable to systems with and without nonlinear interference cancellation. Different to the state-of-the-art rate duality with interference subtraction from Vishwanath et al., the proposed duality is filter-based instead of covariance-based and exploits the arising unitary degree of freedom to decorrelate every point-to-point link. Therefore, it allows for noncooperative stream-wise decoding which reduces complexity and latency. Moreover, the conversion from one domain to the other does not exhibit any dependencies during its computation making it accessible to a parallel implementation instead of a serial one. We additionally derive a rate duality for systems with multi-antenna terminals when linear filtering without interference (pre-)subtraction is applied and the different streams of a single user are not treated as self-interference. Both dualities are based on a framework already applied to a mean-square-error duality between the MAC and the BC. Thanks to this novel rate duality, any rate-based optimization with linear filtering in the BC can now be handled in the dual MAC where the arising expressions lead to more efficient algorithmic solutions than in the BC due to the alignment of the channel and precoder indices.Comment: Submitted to IEEE Globecom 2008; Fixed dimensions of channel matrix H_k and covariance matrix Z_k, slightly modified conclusio

Large Scale Constrained Trajectory Optimization Using Indirect Methods

State-of-the-art direct and indirect methods face significant challenges when solving large scale constrained trajectory optimization problems. Two main challenges when using indirect methods to solve such problems are difficulties in handling path inequality constraints, and the exponential increase in computation time as the number of states and constraints in problem increases. The latter challenge affects both direct and indirect methods. A methodology called the Integrated Control Regularization Method (ICRM) is developed for incorporating path constraints into optimal control problems when using indirect methods. ICRM removes the need for multiple constrained and unconstrained arcs and converts constrained optimal control problems into two-point boundary value problems. Furthermore, it also addresses the issue of transcendental control law equations by re-formulating the problem so that it can be solved by existing numerical solvers for two-point boundary value problems (TPBVP). The capabilities of ICRM are demonstrated by using it to solve some representative constrained trajectory optimization problems as well as a five vehicle problem with path constraints. Regularizing path constraints using ICRM represents a first step towards obtaining high quality solutions for highly constrained trajectory optimization problems which would generally be considered practically impossible to solve using indirect or direct methods. The Quasilinear Chebyshev Picard Iteration (QCPI) method builds on prior work and uses Chebyshev Polynomial series and the Picard Iteration combined with the Modified Quasi-linearization Algorithm. The method is developed specifically to utilize parallel computational resources for solving large TPBVPs. The capabilities of the numerical method are validated by solving some representative nonlinear optimal control problems. The performance of QCPI is benchmarked against single shooting and parallel shooting methods using a multi-vehicle optimal control problem. The results demonstrate that QCPI is capable of leveraging parallel computing architectures and can greatly benefit from implementation on highly parallel architectures such as GPUs. The capabilities of ICRM and QCPI are explored further using a five-vehicle constrained optimal control problem. The scenario models a co-operative, simultaneous engagement of two targets by five vehicles. The problem involves 3DOF dynamic models, control constraints for each vehicle and a no-fly zone path constraint. Trade studies are conducted by varying different parameters in the problem to demonstrate smooth transition between constrained and unconstrained arcs. Such transitions would be highly impractical to study using existing indirect methods. The study serves as a demonstration of the capabilities of ICRM and QCPI for solving large-scale trajectory optimization methods. An open source, indirect trajectory optimization framework is developed with the goal of being a viable contender to state-of-the-art direct solvers such as GPOPS and DIDO. The framework, named beluga, leverages ICRM and QCPI along with traditional indirect optimal control theory. In its current form, as illustrated by the various examples in this dissertation, it has made significant advances in automating the use of indirect methods for trajectory optimization. Following on the path of popular and widely used scientific software projects such as SciPy [1] and Numpy [2], beluga is released under the permissive MIT license [3]. Being an open source project allows the community to contribute freely to the framework, further expanding its capabilities and allow faster integration of new advances to the state-of-the-art