Controlled invariant sets in 2 moves (cis2m) and closed-form implicit representations

This repository is dedicated to the computation of (Robust) Controlled Invariant Sets (RCISs) of Polyhedral Safe Sets for the class of Controllable Discrete-time Time-invariant Linear Systems.

The proposed algorithm operates in two modes:

1. it returns a closed-form expression for an implicit (higher dimensional) representation of an RCIS in the space of states and finite input sequences.
2. it optionally returns an explicit RCIS by projecting the implicit representation to the original state space.

The closed-form expression allows for scalability and is suitable for online applications. Moreover, a hierarchy of RCISs is established, which is parameterized by a positive integer (level of the hierarchy). Currently, we provide a MATLAB and a C++ implementation.

RCISs are used to formally guarantee safe operation of a system. The following video demonstrates how our approach guarantees collision-free trajectories when supervising a Crazyflie 2.0 quadrotor for the task of obstacle avoidance!

Full video here.

Index

• cpp: contains a C++ implementation of the approach.
• matlab: contains a MATLAB implementation of the approach.
• paper-archive: contains the relevant files to replicate the results of our publications.

Related publications

1. T. Anevlavis, Z. Liu, N. Ozay and P. Tabuada,
   “Controlled invariant sets: implicit closed-form representations and applications”,
   arXiv:2107.08566 [math.OC], 2021. ALOT21b

2. Tzanis Anevlavis and Paulo Tabuada,
   “Computing controlled invariant sets in two moves”,
   In 2019 IEEE Conference on Decision and Control (CDC). AT19.

3. Tzanis Anevlavis and Paulo Tabuada,
   “A simple hierarchy for computing controlled invariant sets”,
   In Proceedings of the 23rd ACM International Conference on Hybrid Systems: Computation and Control (HSCC’20). AT20.

4. T. Anevlavis, Z. Liu, N. Ozay and P. Tabuada,
   “An enhanced hierarchy for (robust) controlled invariance”,
   In 2021 American Control Conference (ACC). ALOT21a

5. Luigi Pannocchi, Tzanis Anevlavis, and Paulo Tabuada,
   “Trust your supervisor: quadrotor obstacle avoidance using controlled invariant sets”,
   In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021. (Accepted)

More and cooler examples coming soon! Stay tuned!

For any comments contact Tzanis Anevlavis @ t.anevlavis@ucla.edu.

Citations:

If you used our algorithm for computing controlled invariant sets please cite as:

@misc{anevlavis2021controlled, title={Controlled invariant sets: implicit closed-form representations and applications}, author={Tzanis Anevlavis and Zexiang Liu and Necmiye Ozay and Paulo Tabuada}, year={2021}, eprint={2107.08566}, archivePrefix={arXiv}, primaryClass={math.OC} }