Computing Funnels Using Numerical Optimization Based Falsifiers*

@article{Fejlek2022ComputingFU,
  title={Computing Funnels Using Numerical Optimization Based Falsifiers*},
  author={Jiř{\'i} Fejlek and Stefan Ratschan},
  journal={2022 International Conference on Robotics and Automation (ICRA)},
  year={2022},
  pages={4318-4324}
}
  • Jiří FejlekS. Ratschan
  • Published 23 September 2021
  • Computer Science
  • 2022 International Conference on Robotics and Automation (ICRA)
In this paper, we present an algorithm that computes funnels along trajectories of systems of ordinary differential equations. A funnel is a time-varying set of states containing the given trajectory, for which the evolution from within the set at any given time stays in the funnel. Hence it generalizes the behavior of single trajectories to sets around them, which is an important task, for example, in robot motion planning. In contrast to approaches based on sum-of-squares programming, which… 

Figures and Tables from this paper

Computation of Feedback Control Laws Based on Switched Tracking of Demonstrations

An algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering ordinary differential equations into a goal set is presented.

References

SHOWING 1-10 OF 39 REFERENCES

Invariant Funnels around Trajectories using Sum-of-Squares Programming

A method which exactly certifies sufficient conditions for invariance despite relying on approximate trajectories from numerical integration is presented, and a second method relaxes the constraints of the first by sampling in time.

Control design along trajectories with sums of squares programming

A control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set is presented and certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities.

Funnel libraries for real-time robust feedback motion planning

By explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances, and constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real time in environments with complex geometric constraints.

LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

A feedback motion-planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQR-stabilized trajectories and proves the property of probabilistic coverage.

Path-Following through Control Funnel Functions

An approach to path following using so-called control funnel functions that synthesize both feedback laws using “control funnel functions” that jointly encode the control law as well as its correctness argument over a mathematical model of the vehicle dynamics.

Invariant funnels for underactuated dynamic walking robots: New phase variable and experimental validation

It is shown that for typical models of walking robots the construction of such funnels can be significantly simplified by use of a new phase variable, and the first hardware validation of the resulting funnels on an experimental testbed is provided.

Motion planning with invariant set trees

The planning algorithm Sa-feRRT is introduced, which extends the rapidly-exploring random tree (RRT) algorithm by using feedback control and positively invariant sets to guarantee collision-free closed-loop path tracking.

Learning control lyapunov functions from counterexamples and demonstrations

This approach is able to synthesize relatively simple polynomial control Lyapunov-like functions, and in that process replace the MPC using a guaranteed and computationally less expensive controller.

Control synthesis and verification for a perching UAV using LQR-Trees

It is demonstrated that a recently proposed algorithm called LQR-Trees can generate formal guarantees which verify that a controller generated with trajectory optimization and local linear feedback can achieve the desired perching tolerance from a range of initial conditions.

Neural Lyapunov Control

The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP.