Segway

We started our RTD research with a differential-drive Segway. It is able to navigate unforeseen, random environments consistently without crashing. An RTD implementation for the Segway is available on GitHub.

To learn more about RTD, check out my talk from R:SS '19.

We also enabled RTD to guarantee that it finds optimal trajectory plans in each receding-horizon planning iteration, which we call RTD*. To do this, we make use of a Parallel Constrained Bernstein Algorithm.

Rover

The Segway demonstrates RTD for unstructured scenarios. We have also shown that this trajectory design method can exploit scenario structure with this Rover on a mini road, making lane changes around random obstacles.

Passenger Sedan

With our friends at Ford, we put RTD on a full-sized passenger sedan in the high-fidelity vehicle simulator, CarSim.

Electric Vehicle

In collaboration with the University of Sydney, we put RTD on their Electric Vehicle (EV) platform.

Quadrotor

This work won the ASME Best Student Paper Award at DSCC '19!

To show the flexibility of the RTD way of thinking, we applied to autonomous drone flight. We also used zonotope reachability analysis instead of the sums-of-squares approach from our previous work.

The simulations use a dynamic model of an AscTec Hummingbird, and are entirely created (and rendered) in MATLAB (code here). The hardware demo uses a Parrot Mambo drone with a PhaseSpace motion capture system.

Fetch Manipulator

We have also applied RTD to robotic manipulators -- in particular, a Fetch shown in the video. This leverages our previous zonotope reachability results from the quadrotors, but for the creation (at runtime) of reachable sets of a 6-DOF arm. This enables real-time, safe trajectory planning for arms.

The Geometry of GNSS Uncertainty

I spent my first year at Stanford as a postdoc with Grace Gao's NAV Lab, which has a strong focus on GNSS (Global Navigation Satellite System) for  safe autonomous navigation.

My labmate Ramya and I developed a computationally-efficient method for shadow matching, where one uses a 3-D urban map to identify GNSS shadows, or areas where satellite signals are blocked, to create artificial set-valued measurements that represent uncertain possible receiver positions. Check out Ramya's great talk!

You might notice that our shadow matching method uses polytopes, which can't represent curved convex shapes, such as the Gaussian distribution confidence ellipsoids commonly associated with measurement uncertainty. To solve this challenge, Adam Dai and I created ellipsotopes, a novel set representation that fuses the benefits of polytopes and ellipsoids.

Reachability for Learned Models

Despite the challenges of the COVID-19 pandemic in 2020 and 2021, I've had an amazing opportunity to mentor excellent students.

Simon Shao, Chao Chen, and I used RTD to build a safety layer for a reinforcement learning (RL) agent, which can outperform vanilla RTD. Check out the paper here, and Simon's talk from ICRA 2021!

Edgar Chung, Adam Dai, and Derek Knowles worked with me to compute exact forward reachable sets of feedforward neural networks. Excitingly, this work bridges the gap between verification and training of a neural network. Check out the paper here.