Abstract. We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With "rotor on" and with "rotor off" the corresponding Euler-type equations can be solved, and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera [2].

We study the problem of synthesizing a controller for a robot with a surveillance objective, that is, the robot is required to maintain knowledge of the location of a moving, possibly adversarial target. We formulate this problem as a one-sided partial-information game in which the winning condition for the agent is specified as a temporal logic formula. The specification formalizes the surveillance requirement given by the user, including additional non-surveillance tasks. In order to synthesize a surveillance strategy that meets the specification, we transform the partial-information game into a perfect-information one, using abstraction to mitigate the exponential blow-up typically incurred by such transformations. This enables the use of off-the-shelf tools for reactive synthesis. We use counterexample-guided refinement to automatically achieve abstraction precision that is sufficient to synthesize a surveillance strategy. We evaluate the proposed method on two case-studies, demonstrating its applicability to large state-spaces and diverse requirements.

In this paper, we propose a general approach to derive runtime enforcement implementations for multi-agent systems, called shields, from temporal logical specifications. Each agent of the multiagent system is monitored, and if needed corrected, by the shield, such that a global specification is always satisfied. The different ways of how a shield can interfere with each agent in the system in case of an error introduces the need for quantitative objectives. This work is the first to discuss the shield synthesis problem with quantitative objectives. We provide several cost functions that are utilized in the multi-agent setting and provide methods for the synthesis of cost-optimal shields and fair shields, under the given assumptions on the multi-agent system. We demonstrate the applicability of our approach via a detailed case study on UAV mission planning for warehouse logistics and simulating the shielded multi-agent system on ROS/Gazebo.

Omega-regular objectives in Markov decision processes (MDPs) reduce to reachability: find a policy which maximizes the probability of reaching a target set of states. Given an MDP, an initial distribution, and a target set of states, such a policy can be computed by most probabilistic model checking tools. If the MDP is only partially specified, i.e., some probabilities are unknown, then model-learning techniques can be used to statistically approximate the probabilities and enable the computation of the desired policy. For fully specified MDPs, reducing the size of the MDP translates into faster model checking; for partially specified MDPs, into faster learning. We provide reduction techniques that allow us to remove irrelevant transition probabilities: transition probabilities (known, or to be learned) that do not influence the maximal reachability probability. Among other applications, these reductions can be seen as a pre-processing of MDPs before model checking or as a way to reduce the number of experiments required to obtain a good approximation of an unknown MDP.