Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A second-order chain rule identity for matrix functions is proven to compute the higher-order derivatives to implement cubic-regularized Newton, and a new convergence analysis is provided for cubic-regularized Newton for matrix vector spaces. We demonstrate the applicability of our approach by conducting numerical experiments on both synthetic and real datasets. In our experiments, we formulate a new model for estimating fair and robust covariance matrices in the spirit of the Tyler's M-estimator (TME) model and demonstrate its advantage.

Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use differentiable optimal control for which the gradients of the robot's motion with respect to the parameters are required. We propose a method to efficiently compute these gradients analytically via the differential dynamic programming (DDP) algorithm using sensitivity analysis (SA). We show that we must include second-order dynamics terms when computing the gradients. However, we do not need to include them when computing the motion. We validate our approach on the pendulum and double pendulum systems. Furthermore, we compare against using the derivatives of the iterative linear quadratic regulator (iLQR), which ignores these second-order terms everywhere, on a co-design task for the Kinova arm, where we optimize the link lengths of the robot for a target reaching task. We show that optimizing using iLQR gradients diverges as ignoring the second-order dynamics affects the computation of the derivatives. Instead, optimizing using DDP gradients converges to the same optimum for a range of initial designs allowing our formulation to scale to complex systems.

As an edge intelligence algorithm for multi-device collaborative training, federated learning (FL) can reduce the communication burden but increase the computing load of wireless devices. In contrast, split learning (SL) can reduce the computing load of devices by using model splitting and assignment, but increase the communication burden to transmit intermediate results. In this paper, to exploit the advantages of FL and SL, we propose a hybrid federated split learning (HFSL) framework in wireless networks, which combines the multi-worker parallel update of FL and flexible splitting of SL. To reduce the computational idleness in model splitting, we design a parallel computing scheme for model splitting without label sharing, and theoretically analyze the influence of the delayed gradient caused by the scheme on the convergence speed. Aiming to obtain the trade-off between the training time and energy consumption, we optimize the splitting decision, the bandwidth and computing resource allocation. The optimization problem is multi-objective, and we thus propose a predictive generative adversarial network (GAN)-powered multi-objective optimization algorithm to obtain the Pareto front of the problem. Experimental results show that the proposed algorithm outperforms others in finding Pareto optimal solutions, and the solutions of the proposed HFSL dominate the solution of FL.

This paper considers the simultaneous position and orientation planning of nonholonomic multirobot systems. Different from common researches which only focus on final position constraints, we model the nonholonomic mobile robot as a rigid body and introduce the orientation as well as position constraints for the robot's final states. In other words, robots should not only reach the specified positions, but also point to the desired orientations simultaneously. The challenge of this problem lies in the underactuation of full-state motion planning, since three states need to be planned by mere two control inputs. To this end, we propose a dynamic vector field (DVF) based on the rigid body modeling. Specifically, the dynamics of the robot orientation are brought into the vector field, implying that the vector field is not static on the 2-D plane anymore, but a dynamic one varying with the attitude angle. Hence, each robot can move along the integral curve of the DVF to arrive at the desired position, and in the meantime, the attitude angle can converge to the specified value following the orientation dynamics. Subsequently, by designing a circular vector field under the framework of the DVF, we further study the obstacle avoidance and mutual-robot-collision avoidance in the motion planning. Finally, numerical simulation examples are provided to verify the effectiveness of the proposed methodology.

Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic optimization, which exploits prior knowledge about the geometry of the search space in form of a dissimilarity function. We investigate to which degree the conceptual advantages of Bayesian Optimization can be combined with the computational efficiency of optimistic optimization. By mapping the kernel to a dissimilarity, we obtain an optimistic optimization algorithm for the Bayesian Optimization setting with a run-time of up to $\mathcal{O}(N \log N)$. As a high-level take-away we find that, when using stationary kernels on objectives of relatively low evaluation cost, optimistic optimization can be strongly preferable over Bayesian optimization, while for strongly coupled and parametric models, good implementations of Bayesian optimization can perform much better, even at low evaluation cost. We argue that there is a new research domain between geometric and probabilistic search, i.e. methods that run drastically faster than traditional Bayesian optimization, while retaining some of the crucial functionality of Bayesian optimization.

We present a technique for zero-shot generation of a 3D model using only a target text prompt. Without any 3D supervision our method deforms the control shape of a limit subdivided surface along with its texture map and normal map to obtain a 3D asset that corresponds to the input text prompt and can be easily deployed into games or modeling applications. We rely only on a pre-trained CLIP model that compares the input text prompt with differentiably rendered images of our 3D model. While previous works have focused on stylization or required training of generative models we perform optimization on mesh parameters directly to generate shape, texture or both. To constrain the optimization to produce plausible meshes and textures we introduce a number of techniques using image augmentations and the use of a pretrained prior that generates CLIP image embeddings given a text embedding.

Robots and intelligent systems that sense or interact with the world are increasingly being used to automate a wide array of tasks. The ability of these systems to complete these tasks depends on a large range of technologies such as the mechanical and electrical parts that make up the physical body of the robot and its sensors, perception algorithms to perceive the environment, and planning and control algorithms to produce meaningful actions. Therefore, it is often necessary to consider the interactions between these components when designing an embodied system. This thesis explores work on the task-driven co-optimization of robotics systems in an end-to-end manner, simultaneously optimizing the physical components of the system with inference or control algorithms directly for task performance. We start by considering the problem of optimizing a beacon-based localization system directly for localization accuracy. Designing such a system involves placing beacons throughout the environment and inferring location from sensor readings. In our work, we develop a deep learning approach to optimize both beacon placement and location inference directly for localization accuracy. We then turn our attention to the related problem of task-driven optimization of robots and their controllers. In our work, we start by proposing a data-efficient algorithm based on multi-task reinforcement learning. Our approach efficiently optimizes both physical design and control parameters directly for task performance by leveraging a design-conditioned controller capable of generalizing over the space of physical designs. We then follow this up with an extension to allow for the optimization over discrete morphological parameters such as the number and configuration of limbs. Finally, we conclude by exploring the fabrication and deployment of optimized soft robots.

In this work, we propose a framework for energy-efficient trajectory design of an unmanned aerial vehicle (UAV)-based portable access point (PAP) deployed to serve a set of ground nodes (GNs). In addition to the PAP and GNs, the system consists of a set of intelligent reflecting surfaces (IRSs) mounted on man-made structures to increase the number of bits transmitted per Joule of energy consumed measured as the global energy efficiency (GEE). The GEE trajectory for the PAP is designed by considering the UAV propulsion energy consumption and the Peukert effect of the PAP battery, which represents an accurate battery discharge profile as a non-linear function of the UAV power consumption profile. The GEE trajectory design problem is solved in two phases: in the first, a path for the PAP and feasible positions for the IRS modules are found using a multi-tier circle packing method, and the required IRS phase shift values are calculated using an alternate optimization method that considers the interdependence between the amplitude and phase responses of an IRS element; in the second phase, the PAP flying velocity and user scheduling are calculated using a novel multilap trajectory design algorithm. Numerical evaluations show that: neglecting the Peukert effect overestimates the available flight time of the PAP; after a certain threshold, increasing the battery size reduces the available flight time of the PAP; the presence of IRS modules improves the GEE of the system compared to other baseline scenarios; the multi-lap trajectory saves more energy compared to a single-lap trajectory developed using a combination of sequential convex programming and Dinkelbach algorithm.

Planning a time-optimal trajectory for aerial robots is critical in many drone applications, such as rescue missions and package delivery, which have been widely researched in recent years. However, it still involves several challenges, particularly when it comes to incorporating special task requirements into the planning as well as the aerial robot's dynamics. In this work, we study a case where an aerial manipulator shall hand over a parcel from a moving mobile robot in a time-optimal manner. Rather than setting up the approach trajectory manually, which makes it difficult to determine the optimal total travel time to accomplish the desired task within dynamic limits, we propose an optimization framework, which combines discrete mechanics and complementarity constraints (DMCC) together. In the proposed framework, the system dynamics is constrained with the discrete variational Lagrangian mechanics that provides reliable estimation results also according to our experiments. The handover opportunities are automatically determined and arranged based on the desired complementarity constraints. Finally, the performance of the proposed framework is verified with numerical simulations and hardware experiments with our self-designed aerial manipulators.

Black-box optimization has potential in numerous applications such as hyperparameter optimization in machine learning and optimization in design of experiments. Ising machines are useful for binary optimization problems because variables can be represented by a single binary variable of Ising machines. However, conventional approaches using an Ising machine cannot handle black-box optimization problems with non-binary values. To overcome this limitation, we propose an approach for integer-variable black-box optimization problems by using Ising/annealing machines and factorization machines in cooperation with three different integer-encoding methods. The performance of our approach is numerically evaluated with different encoding methods using a simple problem of calculating the energy of the hydrogen molecule in the most stable state. The proposed approach can calculate the energy using any of the integer-encoding methods. However, one-hot encoding is useful for problems with a small size.