Imitation learning (IL) has proven to be an effective method for learning good policies from expert demonstrations. Adversarial imitation learning (AIL), a subset of IL methods, is particularly promising, but its theoretical foundation in the presence of unknown transitions has yet to be fully developed. This paper explores the theoretical underpinnings of AIL in this context, where the stochastic and uncertain nature of environment transitions presents a challenge. We examine the expert sample complexity and interaction complexity required to recover good policies. To this end, we establish a framework connecting reward-free exploration and AIL, and propose an algorithm, MB-TAIL, that achieves the minimax optimal expert sample complexity of $\widetilde{O} (H^{3/2} |S|/\varepsilon)$ and interaction complexity of $\widetilde{O} (H^{3} |S|^2 |A|/\varepsilon^2)$. Here, $H$ represents the planning horizon, $|S|$ is the state space size, $|A|$ is the action space size, and $\varepsilon$ is the desired imitation gap. MB-TAIL is the first algorithm to achieve this level of expert sample complexity in the unknown transition setting and improves upon the interaction complexity of the best-known algorithm, OAL, by $O(H)$. Additionally, we demonstrate the generalization ability of MB-TAIL by extending it to the function approximation setting and proving that it can achieve expert sample and interaction complexity independent of $|S|$

This thesis studies the domain of collective robotics, and more particularly the optimization problems of multirobot systems in the context of exploration, path planning and coordination. It includes two contributions. The first one is the use of the Butterfly Optimization Algorithm (BOA) to solve the Unknown Area Exploration problem with energy constraints in dynamic environments. This algorithm was never used for solving robotics problems before, as far as we know. We proposed a new version of this algorithm called xBOA based on the crossover operator to improve the diversity of the candidate solutions and speed up the convergence of the algorithm. The second contribution is the development of a new simulation framework for benchmarking dynamic incremental problems in robotics such as exploration tasks. The framework is made in such a manner to be generic to quickly compare different metaheuristics with minimum modifications, and to adapt easily to single and multi-robot scenarios. Also, it provides researchers with tools to automate their experiments and generate visuals, which will allow them to focus on more important tasks such as modeling new algorithms. We conducted a series of experiments that showed promising results and allowed us to validate our approach and model.

This paper proposes a framework for generating fast, smooth and predictable braking manoeuvers for a controlled robot. The proposed framework integrates two approaches to obtain feasible modal limits for designing braking trajectories. The first approach is real-time capable but conservative considering the usage of the available feasible actuator control region, resulting in longer braking times. In contrast, the second approach maximizes the used braking control inputs at the cost of requiring more time to evaluate larger, feasible modal limits via optimization. Both approaches allow for predicting the robot's stopping trajectory online. In addition, we also formulated and solved a constrained, nonlinear final-time minimization problem to find optimal torque inputs. The optimal solutions were used as a benchmark to evaluate the performance of the proposed predictable braking framework. A comparative study was compiled in simulation versus a classical optimal controller on a 7-DoF robot arm with only three moving joints. The results verified the effectiveness of our proposed framework and its integrated approaches in achieving fast robot braking manoeuvers with accurate online predictions of the stopping trajectories and distances under various braking settings.

Real-time computation of optimal control is a challenging problem and, to solve this difficulty, many frameworks proposed to use learning techniques to learn (possibly sub-optimal) controllers and enable their usage in an online fashion. Among these techniques, the optimal motion framework is a simple, yet powerful technique, that obtained success in many complex real-world applications. The main idea of this approach is to take advantage of dynamic motion primitives, a widely used tool in robotics to learn trajectories from demonstrations. While usually these demonstrations come from humans, the optimal motion framework is based on demonstrations coming from optimal solutions, such as the ones obtained by numeric solvers. As usual in many learning techniques, a drawback of this approach is that it is hard to estimate the suboptimality of learned solutions, since finding easily computable and non-trivial upper bounds to the error between an optimal solution and a learned solution is, in general, unfeasible. However, we show in this paper that it is possible to estimate this error for a broad class of problems. Furthermore, we apply this estimation technique to achieve a novel and more efficient sampling scheme to be used within the optimal motion framework, enabling the usage of this framework in some scenarios where the computational resources are limited.

Complex dexterous manipulations require switching between prehensile and non-prehensile grasps, and sliding and pivoting the object against the environment. This paper presents a manipulation planner that is able to reason about diverse changes of contacts to discover such plans. It implements a hybrid approach that performs contact-implicit trajectory optimization for pivoting and sliding manipulation primitives and sampling-based planning to change between manipulation primitives and target object poses. The optimization method, simultaneous trajectory optimization and contact selection (STOCS), introduces an infinite programming framework to dynamically select from contact points and support forces between the object and environment during a manipulation primitive. To sequence manipulation primitives, a sampling-based tree-growing planner uses STOCS to construct a manipulation tree. We show that by using a powerful trajectory optimizer, the proposed planner can discover multi-modal manipulation trajectories involving grasping, sliding, and pivoting within a few dozen samples. The resulting trajectories are verified to enable a 6 DoF manipulator to manipulate physical objects successfully.

Target tracking with a mobile robot has numerous significant applications in both civilian and military. Practical challenges such as limited field-of-view, obstacle occlusion, and system uncertainty may all adversely affect tracking performance, yet few existing works can simultaneously tackle these limitations. To bridge the gap, we introduce the concept of belief-space probability of detection (BPOD) to measure the predictive visibility of the target under stochastic robot and target states. An Extended Kalman Filter variant incorporating BPOD is developed to predict target belief state under uncertain visibility within the planning horizon. Furthermore, we propose a computationally efficient algorithm to uniformly calculate both BPOD and the chance-constrained collision risk by utilizing linearized signed distance function (SDF), and then design a two-stage strategy for lightweight calculation of SDF in sequential convex programming. Building upon these treatments, we develop a real-time, non-myopic trajectory planner for visibility-aware and safe target tracking in the presence of system uncertainty. The effectiveness of the proposed approach is verified by both simulations and real-world experiments.

Reliability Assessment Commitment (RAC) Optimization is increasingly important in grid operations due to larger shares of renewable generations in the generation mix and increased prediction errors. Independent System Operators (ISOs) also aim at using finer time granularities, longer time horizons, and possibly stochastic formulations for additional economic and reliability benefits. The goal of this paper is to address the computational challenges arising in extending the scope of RAC formulations. It presents RACLearn that (1) uses a Graph Neural Network (GNN) based architecture to predict generator commitments and active line constraints, (2) associates a confidence value to each commitment prediction, (3) selects a subset of the high-confidence predictions, which are (4) repaired for feasibility, and (5) seeds a state-of-the-art optimization algorithm with feasible predictions and active constraints. Experimental results on exact RAC formulations used by the Midcontinent Independent System Operator (MISO) and an actual transmission network (8965 transmission lines, 6708 buses, 1890 generators, and 6262 load units) show that the RACLearn framework can speed up RAC optimization by factors ranging from 2 to 4 with negligible loss in solution quality.

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural networks for solving routing problems. However, such methods typically produce sequences of vertices, which makes it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges, as in various spanning tree problems. In this paper, we propose NeuroPrim, a novel framework for solving various spanning tree problems by defining a Markov Decision Process (MDP) for general combinatorial optimization problems on graphs. Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE. We apply our framework to three difficult problems on Euclidean space: the Degree-constrained Minimum Spanning Tree (DCMST) problem, the Minimum Routing Cost Spanning Tree (MRCST) problem, and the Steiner Tree Problem in graphs (STP). Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices. Additionally, we find that our model has strong generalization ability, with no significant degradation observed on problem instances as large as 1000. Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can handle general nonlinear system dynamics, bounded adversarial system disturbances, and state and input constraints. However, it involves solving a PDE, whose computational and memory complexity scales exponentially with respect to the state dimensionality, making its direct use on large-scale systems intractable. A recently proposed method called DeepReach overcomes this challenge by leveraging a sinusoidal neural PDE solver for high-dimensional reachability problems, whose computational requirements scale with the complexity of the underlying reachable tube rather than the state space dimension. Unfortunately, neural networks can make errors and thus the computed solution may not be safe, which falls short of achieving our overarching goal to provide formal safety assurances. In this work, we propose a method to compute an error bound for the DeepReach solution. This error bound can then be used for reachable tube correction, resulting in a safe approximation of the true reachable tube. We also propose a scenario-based optimization approach to compute a probabilistic bound on this error correction for general nonlinear dynamical systems. We demonstrate the efficacy of the proposed approach in obtaining probabilistically safe reachable tubes for high-dimensional rocket-landing and multi-vehicle collision-avoidance problems.

Force modulation of robotic manipulators has been extensively studied for several decades. However, it is not yet commonly used in safety-critical applications due to a lack of accurate interaction contact modeling and weak performance guarantees - a large proportion of them concerning the modulation of interaction forces. This study presents a high-level framework for simultaneous trajectory optimization and force control of the interaction between a manipulator and soft environments, which is prone to external disturbances. Sliding friction and normal contact force are taken into account. The dynamics of the soft contact model and the manipulator are simultaneously incorporated in a trajectory optimizer to generate desired motion and force profiles. A constrained optimization framework based on Alternative Direction Method of Multipliers (ADMM) has been employed to efficiently generate real-time optimal control inputs and high-dimensional state trajectories in a Model Predictive Control fashion. Experimental validation of the model performance is conducted on a soft substrate with known material properties using a Cartesian space force control mode. Results show a comparison of ground truth and real-time model-based contact force and motion tracking for multiple Cartesian motions in the valid range of the friction model. It is shown that a contact model-based motion planner can compensate for frictional forces and motion disturbances and improve the overall motion and force tracking accuracy. The proposed high-level planner has the potential to facilitate the automation of medical tasks involving the manipulation of compliant, delicate, and deformable tissues.