We then use MPC to find a control sequence that minimises the expected long-term cost. In particular, we propose to learn a probabilistic transition model using Gaussian Processes (GPs) to incorporate model uncertainty into longterm predictions, thereby, reducing the impact of model errors. To reduce the number of system interactions while simultaneously handling constraints, we propose a modelbased RL framework based on probabilistic Model Predictive Control (MPC). A large number of interactions may be impractical in many real-world applications, such as robotics, and many practical systems have to obey limitations in the form of state space or control constraints. However, the majority of autonomous RL algorithms require a large number of interactions with the environment. Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. We implement and evaluate our approach on controllers trained for several benchmark control problems. It produces bounds on the probability of safe operation of the controller for different initial configurations and identifies regions where correct behaviour can be guaranteed. Our approach is based on the iterative construction of a formal abstraction of a controller’s execution in an environment, and leverages probabilistic model checking of Markov decision processes to produce probabilistic guarantees on safe behaviour over a finite time horizon. We propose MOSAIC, an algorithm for measuring the safety of deep reinforcement learning controllers in stochastic settings. Rigorous testing of these controllers is challenging, particularly when they operate in probabilistic environments due to, for example, hardware faults or noisy sensors. Time complexity is known for classic algorithms, so the presented algorithm is compared analytically.ĭeep reinforcement learning has been successfully applied to many control tasks, but the application of such controllers in safety-critical scenarios has been limited due to safety concerns. Different benchmark scenarios are used to evaluate the performance of the algorithm relative to the first two classes of algorithms: GAMOPP (genetic algorithm for multi-objective path planning), a representative heuristic algorithm, as well as RRT (rapidly-exploring random tree) and PRM (probabilistic road map), two well-known probabilistic algorithms. The performance of the algorithm is evaluated relative to three major classes of algorithms: heuristic, probabilistic, and classic. It is proven that the SPP algorithm can find the optimal path in O(nn r2 ) time, where n is the number of vertices of all polygons and n ̓ is the number of vertices that are considered in constructing the path network (n ̓ ≤ n). It has the capability of eliminating some of the polygons that do not play any role in constructing the optimal path. This algorithm is designed for environments that are populated sparsely with convex and nonconvex polygonal obstacles. The SPP algorithm generates a safe, smooth and obstacle-free path that has a desired distance from each obstacle. Then it finds the shortest path from start to goal point within this network. The proposed algorithm, which is called the shortest possible path (SPP) algorithm, constructs a network of lines connecting the vertices of the obstacles and the locations of the start and goal points which is smaller than the network generated by the visibility graph. We apply the DMPC algorithm to the motion planning of an autonomous vehicle with nonlinear dynamics.Ī novel, exact algorithm is presented to solve the path planning problem that involves finding the shortest collision-free path from a start to a goal point in a two-dimensional environment containing convex and non-convex obstacles. Theoretical analysis of the algorithm is presented, proving that the quality of the trajectory does not worsen with each new iteration, as well as providing bounds on the complexity. DMPC (1) provides an approach to merge both the model-based and black-box systems (2) can cope with very little data and is sample efficient, building its solutions based on recently generated trajectories and (3) improves its cost in each iteration until converging to an optimal trajectory, typically needing only a few trials even for nonlinear dynamics and objectives. a machine learning technique, that predicts the value of the unknown functions for a given trajectory. It is assumed that there is an exogenous ``black box'' system, e.g. This work presents DMPC (Data-and Model-Driven Predictive Control) to solve control problems in which some of the constraints or parts of the objective function are known, while others are entirely unknown to the controller.
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