Projects
Robot-Assisted Corneal Surgery
In this project, we aim to develop an autonomous system capable of performing high-precision corneal surgery. The surgery we try to perform is called DALK. My work is to plan how to place the needle preciously into the cornea to a certain depth to increase surgery success rate. Although this task sounds easy, it is indeed extremely difficult to model the deformation of the needle and the cornea during insertion. We use a data-driven approach to learn the dynamics and design a model predictive controller (MPC) to calculate the optimal path.
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Data-Driven Motion Planning
Optimization is generally slow and unreliable except for convex problems. Random-restart relieves some reliability issue but is too slow to be used in real-time. However, offline computation is relatively cheap and easily accessible nowadays. The data-driven planning project tries to investigate what machine learning methods can be used and how much they can help to speed up optimization. We start from a nearest neighbor approach and develop the Nearest Neighbor Optimal Control (NNOC) approach. It achieves one or two orders of magnitude speedup in the benchmark problems. However, it does not scale well. Later work includes using neural network to learn the optimal trajectories and use Mixture of Experts (MOE) model to handle the function discontinuity issue.
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Bilevel Optimization
In some optimization problems encountered in robotic application, the nonlinear problem has some convex sub-problems. For example, the classical minimum-jerk drone trajectory optimization problem is nonconvex if the flight time has to be optimized. But for a given fixed flight time, the problem is convex. The idea is thus to choose some flight time, solve the convex problem, and update the flight time towards optimality. This can be categorized into a bilevel optimization problem: the outer problem optimizes flight time and the inner problem optimizes the path shape. We use sensitivity analysis of optimization problems to provide an analytic gradient to the outer problem by solving the inner problem. By this decomposition, untrackable nonconvex problem becomes trackable and we an efficient and reliable optimizer for this problem. This idea is also extended to time-optimal trajectory optimization problems for field robots.
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Learning from Execution
Robot motions are subject to constraints such as feasible friction, maximum speed, and collision avoidance. However, there is a tradeoff between motion safety and motion aggressiveness. This project considers hard-to-model constraints and generate optimal motions subject to these constraints. A simple yet useful constraint type is the convex constraint and it can model such as feasible friction from contact. This project iteratively learns convex constraints from plan execution. Feedback of plan execution success is used as feedback to adjust the constraints. Through this process eventually an aggressive yet safe plan can be computed.
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