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.

Haegu Lee, Yitaek Kim, Christoffer Sloth

Smoothed implicit contact dynamics enables gradient-based planning and control for contact-rich tasks without predefined mode sequences. However, safety-critical control remains challenging because implicit contact dynamics makes safety-filter design nontrivial. The smoothing parameter $κ$ relaxes contact complementarity constraints, which makes the dynamics smooth but affects the contact force. This paper provides a method for bounding the actual contact force despite the use of relaxed complementarity constraints. We show that constraint violations can be non-monotonic in $κ$. Smaller $κ$ reduces force-approximation error, but it does not necessarily improve safety performance. To address this issue, we introduce boundary-focused rollouts to screen $κ$ by comparing the safety margin with the approximation error. We then develop a discrete-time control barrier function (CBF) framework based on a first-order Taylor approximation of the implicitly defined contact force. To account for possible force under-prediction, we augment the resulting safety constraint with a fixed robust margin. Simulations on four contact-rich systems show that the proposed method eliminates force violations observed under a standard CBF.

Chengyandan Shen, Christoffer Sloth

This paper proposes an exploration-efficient Deep Reinforcement Learning with Reference policy (DRLR) framework for learning robotics tasks that incorporates demonstrations. The DRLR framework is developed based on an algorithm called Imitation Bootstrapped Reinforcement Learning (IBRL). We propose to improve IBRL by modifying the action selection module. The proposed action selection module provides a calibrated Q-value, which mitigates the bootstrapping error that otherwise leads to inefficient exploration. Furthermore, to prevent the RL policy from converging to a sub-optimal policy, SAC is used as the RL policy instead of TD3. The effectiveness of our method in mitigating bootstrapping error and preventing overfitting is empirically validated by learning two robotics tasks: bucket loading and open drawer, which require extensive interactions with the environment. Simulation results also demonstrate the robustness of the DRLR framework across tasks with both low and high state-action dimensions, and varying demonstration qualities. To evaluate the developed framework on a real-world industrial robotics task, the bucket loading task is deployed on a real wheel loader. The sim2real results validate the successful deployment of the DRLR framework.

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.