Bio

I am a Ph.D candidate in robotics and optimization at Stanford University.

My research focuses on developing fast optimization algorithms for simulation, planning, and control for robotic systems. I am designing and implementing differentiable physics tools for trajectory tracking, planning and reinforcement learning tasks in robotic locomotion and manipulation. Previously, I implemented optimization algorithms enabling game-theoretic reasoning for autonomous vehicles.

Portfolio

Unified collision detection and contact dynamics

With Silico, we unified collision detection and contact dynamics into a single optimization problem. With this novel formulation, we can smoothly differentiate through contact dynamics for objects of arbitrary shapes. Previous differentiable physics formulations were limited to simple shape primitives.

Grasping behavior obtained with a sampling-based planner leveraging smoothly differentiable collision detection and contact simulation.

Differentiable physics engine

With Dojo, we took a physics- and optimization-first approach to address some of the limitations of the current physics engines. In particular, we can provide informative gradients through contact dynamics. Contrary to simulators relying on soft-contact models, Dojo can simulate hard contact interactions. Additionally, it does not need to approximate the friction cone to simulate sliding behavior.

Differentiable simulation of a Unitree A1 quadruped in Dojo.

Simulating neural objects contact interactions

We proposed a simple approach to neural object contact simulation. By augmenting a neural object with dynamics properties such as mass, inertia, coefficient of friction, we can simulate the object interaction with the environment, other objects or even oter neural objects.

Sampling the neural object density field is the first step before simulating contact interactions.

Optimizing through contact

We leveraged differentiable contact simulation for control through contact. We embedded a differentiable physics engine into an online optimization pipeline.

The quadruped trots while we introduce some disturbances.

Learning Objective Functions

We coupled an online estimation technique and a fast dynamic game solver to allow an autonomous driving vehicle to optimize its trajectory while learning the objective functions of the cars in its surroundings. It allows the autonomous vehicle to quickly identify the desired speed, desired lane and aggresiveness level of the vehicles it is interacting with. This gained information further improves the trajectory prediction ability of the autonomous vehicle.

Orange estimates if blue will accelerate of slow down to let it go first.

Solving Dynamic Games

We developed fast solver for constrained dynamic games and applied it to complex autonomous driving scenarios. It generates complex driving behaviors where vehicles negotiate and share the responsibility for avoiding collisions.

Vehicles negotiating right-of-way on a highway ramp.

Computing Robustness Guarantees

We developed an algorithm relying on a novel sampling-based technique to efficiently compute regions of finite time invariance, commonly refered to as “invariant funnels”. We apply our algorithm to a spacecraft atmospheric entry problem where the goal is to identify the landing zone that the spacecraft is guaranteed to reach under uncertain atmospheric disturbances.

Trajectory funnel of a probe landing on Mars.

Optimizing nonsmooth objective functions

We applied the Alternating Direction Method of Multipliers (ADMM) to solve optimal control problems with L1-norm cost. One application of this work is minimum-fuel trajectory optimization for satellites.

Fuel-optimal rendez-vous trajectory between two satellites.