A neural network-based framework is developed and experimentally demonstrated for the problem of estimating the shape of a soft continuum arm (SCA) from noisy measurements of the pose at a finite number of locations along the length of the arm. The neural network takes as input these measurements and produces as output a finitedimensional approximation of the strain, which is further used to reconstruct the infinite-dimensional smooth posture. This problem is important for various soft robotic applications. It is challenging due to the flexible aspects that lead to the infinitedimensional reconstruction problem for the continuous posture and strains. Because of this, past solutions to this problem are computationally intensive. The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy. The framework is evaluated on two testbeds: a simulated octopus muscular arm and a physical BR2 pneumatic soft manipulator.

This paper is concerned with the problem of estimating (interpolating and smoothing) the shape (pose and the six modes of deformation) of a slender flexible body from multiple camera measurements. This problem is important in both biology, where slender, soft, and elastic structures are ubiquitously encountered across species, and in engineering, particularly in the area of soft robotics. The proposed mathematical formulation for shape estimation is physics-informed, based on the use of the special Cosserat rod theory whose equations encode slender body mechanics in the presence of bending, shearing, twisting and stretching. The approach is used to derive numerical algorithms which are experimentally demonstrated for fiber reinforced and cable-driven soft robot arms. These experimental demonstrations show that the methodology is accurate (<5 mm error, three times less than the arm diameter) and robust to noise and uncertainties.

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated methods in (Wibisono et al., 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. An important special case is considered where the objective functional is the relative entropy. For this case, two numerical approximations are presented to implement the Hamilton’s equations as a system of N interacting particles. The algorithm is numerically illustrated and compared with the MCMC and Hamiltonian MCMC algorithms.

This paper is concerned with the problem of representing and learning a linear transformation using a linear neural network. In recent years, there is a growing interest in the study of such networks, in part due to the successes of deep learning. The main question of this body of research (and also of our paper) is related to the existence and optimality properties of the critical points of the mean-squared loss function. An additional primary concern of our paper pertains to the robustness of these critical points in the face of (a small amount of) regularization. An optimal control model is introduced for this purpose and a learning algorithm (backprop with weight decay) derived for the same using the Hamilton's formulation of optimal control. The formulation is used to provide a complete characterization of the critical points in terms of the solutions of a nonlinear matrix-valued equation, referred to as the characteristic equation. Analytical and numerical tools from bifurcation theory are used to compute the critical points via the solutions of the characteristic equation.

This work considers the optimal scheduling problem for a campus central plant equipped with a bank of multiple electrical chillers and a thermal energy storage (TES). Typically, the chillers are operated in ON/OFF modes to charge TES and supply chilled water to satisfy the campus cooling demands. A bilinear model is established to describe the system dynamics of the central plant. A model predictive control (MPC) problem is formulated to obtain optimal set-points to satisfy the campus cooling demands and minimize daily electricity cost. At each time step, the MPC problem is represented as a large-scale mixed-integer nonlinear programming problem. We propose a heuristic algorithm to obtain suboptimal solutions for it via dynamic programming (DP) and mixed integer linear programming (MILP). The system dynamics is linearized along the simulated trajectories of the system. The optimal TES operation profile is obtained by solving a DP problem at every horizon, and the optimal chiller operations are obtained by solving an MILP problem at every time step with a fixed TES operation profile. Simulation results show desired performance and computational tractability of the proposed algorithm. This work was motivated by the supervisory control need for a campus central plant. Plant operators have to decide a scheduling strategy to mix and match various chillers with a thermal energy storage to satisfy the campus cooling demands, while minimizing the operation cost. This work mathematically characterizes the system dynamics of a campus central plant and establishes a linear model to predict campus cooling load. It proposes a model predictive control (MPC) strategy to optimally schedule the campus central plant based on plant system dynamics and predicted campus cooling load. A heuristic algorithm is proposed to obtain suboptimal solutions for the MPC problem. The effectiveness and efficiency of the proposed approach are well demonstrated for the central plant at the University of California, Irvine.