Christoffer Sloth

Christoffer Sloth, Rafael Wisniewski

In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse-Smale systems and complete and refinable abstractions for linear systems are proved.

Christoffer Sloth, Rafael Wisniewski

This paper proposes a method for abstracting control systems by timed game automata, and is aimed at obtaining automatic controller synthesis. The proposed abstraction is based on partitioning the state space of a control system using positive and negative invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the control system is transversal to the facets of the cells, which induces some desirable properties of the abstraction. To allow a rich class of control systems to be abstracted, the update maps of the timed game automaton are extended. Conditions on the partitioning of the state space and the control are set up to obtain sound abstractions. Finally, an example is provided to demonstrate the method applied to a control problem related to navigation.

Christoffer Sloth

This paper presents a nonnegative polynomial that cannot be represented with nonnegative coefficients in the simplicial Bernstein basis by subdividing the standard simplex. The example shows that Bernstein Theorem cannot be extended to certificates of nonnegativity for polynomials with zeros at isolated points.

Rasmus Laurvig Haugaard, Jeppe Langaa, Christoffer Sloth et al.

This paper demonstrates a visual servoing method which is robust towards uncertainties related to system calibration and grasping, while significantly reducing the peg-in-hole time compared to classical methods and recent attempts based on deep learning. The proposed visual servoing method is based on peg and hole point estimates from a deep neural network in a multi-cam setup, where the model is trained on purely synthetic data. Empirical results show that the learnt model generalizes to the real world, allowing for higher success rates and lower cycle times than existing approaches.