In air-ground collaboration scenarios without GPS and prior maps, the relative positioning of drones and unmanned ground vehicles (UGVs) has always been a challenge. For a drone equipped with monocular camera and an UGV equipped with LiDAR as an external sensor, we propose a robust and real-time relative pose estimation method (LVCP) based on the tight coupling of vision and LiDAR point cloud information, which does not require prior information such as maps or precise initial poses. Given that large-scale point clouds generated by 3D sensors has more accurate spatial geometric information than the feature point cloud generated by image, we utilize LiDAR point clouds to correct the drift in visual-inertial odometry (VIO) when the camera undergoes significant shaking or the IMU has a low signal-to-noise ratio. To achieve this, we propose a novel coarse-to-fine framework for LiDAR-vision collaborative localization. In this framework, we construct point-plane association based on spatial geometric information, and innovatively construct a point-aided Bundle Adjustment (BA) problem as the backend to simultaneously estimate the relative pose of the camera and LiDAR and correct the VIO drift. In this process, we propose a particle swarm optimization (PSO) based sampling algorithm to complete the coarse estimation of the current camera-LiDAR pose. In this process, the initial pose of the camera used for sampling is obtained based on VIO propagation, and the valid feature-plane association number (VFPN) is used to trigger PSO-sampling process. Additionally, we propose a method that combines Structure from Motion (SFM) and multi-level sampling to initialize the algorithm, addressing the challenge of lacking initial values.

Constrained Reinforcement Learning (CRL) tackles sequential decision-making problems where agents are required to achieve goals by maximizing the expected return while meeting domain-specific constraints, which are often formulated as expected costs. In this setting, policy-based methods are widely used since they come with several advantages when dealing with continuous-control problems. These methods search in the policy space with an action-based or parameter-based exploration strategy, depending on whether they learn directly the parameters of a stochastic policy or those of a stochastic hyperpolicy. In this paper, we propose a general framework for addressing CRL problems via gradient-based primal-dual algorithms, relying on an alternate ascent/descent scheme with dual-variable regularization. We introduce an exploration-agnostic algorithm, called C-PG, which exhibits global last-iterate convergence guarantees under (weak) gradient domination assumptions, improving and generalizing existing results. Then, we design C-PGAE and C-PGPE, the action-based and the parameter-based versions of C-PG, respectively, and we illustrate how they naturally extend to constraints defined in terms of risk measures over the costs, as it is often requested in safety-critical scenarios. Finally, we numerically validate our algorithms on constrained control problems, and compare them with state-of-the-art baselines, demonstrating their effectiveness.

This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin-Huxley model with a practically relevant number of parameters.

Robust optimisation is a well-established framework for optimising functions in the presence of uncertainty. The inherent goal of this problem is to identify a collection of inputs whose outputs are both desirable for the decision maker, whilst also being robust to the underlying uncertainties in the problem. In this work, we study the multi-objective case of this problem. We identify that the majority of all robust multi-objective algorithms rely on two key operations: robustification and scalarisation. Robustification refers to the strategy that is used to account for the uncertainty in the problem. Scalarisation refers to the procedure that is used to encode the relative importance of each objective to a scalar-valued reward. As these operations are not necessarily commutative, the order that they are performed in has an impact on the resulting solutions that are identified and the final decisions that are made. The purpose of this work is to give a thorough exposition on the effects of these different orderings and in particular highlight when one should opt for one ordering over the other. As part of our analysis, we showcase how many existing risk concepts can be integrated into the specification and solution of a robust multi-objective optimisation problem. Besides this, we also demonstrate how one can principally define the notion of a robust Pareto front and a robust performance metric based on our ``robustify and scalarise'' methodology. To illustrate the efficacy of these new ideas, we present two insightful case studies which are based on real-world data sets.

Contemporary robots have become exceptionally skilled at achieving specific tasks in structured environments. However, they often fail when faced with the limitless permutations of real-world unstructured environments. This motivates robotics methods which learn from experience, rather than follow a pre-defined set of rules. In this thesis, we present a range of learning-based methods aimed at enabling robots, operating in dynamic and unstructured environments, to better understand their surroundings, anticipate the actions of others, and take informed actions accordingly. In the first part of the thesis, we investigate methods which leverage learning to represent the structure and motion in a robot's operating environment, in a continuous manner.

Optimizing the fuel cycle cost through the optimization of nuclear reactor core loading patterns involves multiple objectives and constraints, leading to a vast number of candidate solutions that cannot be explicitly solved. To advance the state-of-the-art in core reload patterns, we have developed methods based on Deep Reinforcement Learning (DRL) for both single- and multi-objective optimization. Our previous research has laid the groundwork for these approaches and demonstrated their ability to discover high-quality patterns within a reasonable time frame. On the other hand, stochastic optimization (SO) approaches are commonly used in the literature, but there is no rigorous explanation that shows which approach is better in which scenario. In this paper, we demonstrate the advantage of our RL-based approach, specifically using Proximal Policy Optimization (PPO), against the most commonly used SO-based methods: Genetic Algorithm (GA), Parallel Simulated Annealing (PSA) with mixing of states, and Tabu Search (TS), as well as an ensemble-based method, Prioritized Replay Evolutionary and Swarm Algorithm (PESA). We found that the LP scenarios derived in this paper are amenable to a global search to identify promising research directions rapidly, but then need to transition into a local search to exploit these directions efficiently and prevent getting stuck in local optima. PPO adapts its search capability via a policy with learnable weights, allowing it to function as both a global and local search method. Subsequently, we compared all algorithms against PPO in long runs, which exacerbated the differences seen in the shorter cases. Overall, the work demonstrates the statistical superiority of PPO compared to the other considered algorithms.

The concept of robustness is of paramount importance across a variety of fields, particularly those involving practical statistical parameter estimation based on real-world observations. However, robust estimation techniques introduced in various methodologies aim to achieve different objectives, and each technique has been examined within individual frameworks. It is crucial to reexamine the purpose behind robust estimation and provide an integrated perspective across disciplinary boundaries. To facilitate this, this study initially classifies the goals of robust estimation methods into three categories: resistance to (1) outlier contamination (see, e.g., Huber and Ronchetti (1981) and Hampel et al. (1986)), (2) user-specified imaginary dataset-perturbation (see, e.g., Ben-Tal and Nemirovski (2002) and Biggio et al. (2013)), and (3) model misspecification. Notably, (3) can be addressed using expressive models in certain cases; (3) will be discussed later but will not be the main focus. Therefore, this study primarily focuses on the following two categories within the context of linear regression: (1) Outlier-resistance. Outliers are data points that deviate significantly from the overall trend of the other observations in a dataset. Since the presence of outliers can affect statistical parameter estimation, potentially leading to unintended results, outlier-resistant estimation has been a focus for many decades (Huber and Ronchetti, 1981; Hampel et al., 1986; Maronna et al., 2006) mainly in the field of statistics. Originating from the works of Tukey (1960) and Huber (1964), many outlier-resistant estimations are designed by modifying the loss function.

Free-form structural forms are widely used to design spatial structures for their irregular spatial morphology. Current free-form form-finding methods cannot adequately meet the material properties, structural requirements or construction conditions, which brings the deviation between the initial 3D geometric design model and the constructed free-form structure. Thus, the main focus of this paper is to improve the rationality of free-form morphology considering multiple objectives in line with the characteristics and constraints of material. In this paper, glued laminated timber is selected as a case. Firstly, machine learning is adopted based on the predictive capability. By selecting a free-form timber grid structure and following the principles of NURBS, the free-form structure is simplified into free-form curves. The transformer is selected to train and predict the curvatures of the curves considering the material characteristics. After predicting the curvatures, the curves are transformed into vectors consisting of control points, weights, and knot vectors. To ensure the constructability and robustness of the structure, minimising the mass of the structure, stress and strain energy are the optimisation objectives. Two parameters (weight and the z-coordinate of the control points) of the free-from morphology are extracted as the variables of the free-form morphology to conduct the optimisation. The evaluation algorithm was selected as the optimal tool due to its capability to optimise multiple parameters. While optimising the two variables, the mechanical performance evaluation indexes such as the maximum displacement in the z-direction are demonstrated in the 60th step. The optimisation results for structure mass, stress and strain energy after 60 steps show the tendency of oscillation convergence, which indicates the efficiency of the proposal multi-objective optimisation.

As fully-actuated systems, omnidirectional multirotor aerial vehicles (OMAVs) have more flexible maneuverability and advantages in aggressive flight in cluttered environments than traditional underactuated MAVs. %Due to the high dimensionality of configuration space, making the designed trajectory generation algorithm efficient is challenging. This paper aims to achieve safe flight of OMAVs in cluttered environments. Considering existing static obstacles, an efficient optimization-based framework is proposed to generate 6-D $SE(3)$ trajectories for OMAVs. Given the kinodynamic constraints and the 3D collision-free region represented by a series of intersecting convex polyhedra, the proposed method finally generates a safe and dynamically feasible 6-D trajectory. First, we parameterize the vehicle's attitude into a free 3D vector using stereographic projection to eliminate the constraints inherent in the $SO(3)$ manifold, while the complete $SE(3)$ trajectory is represented as a 6-D polynomial in time without inherent constraints. The vehicle's shape is modeled as a cuboid attached to the body frame to achieve whole-body collision evaluation. Then, we formulate the origin trajectory generation problem as a constrained optimization problem. The original constrained problem is finally transformed into an unconstrained one that can be solved efficiently. To verify the proposed framework's performance, simulations and real-world experiments based on a tilt-rotor hexarotor aerial vehicle are carried out.