Model predictive control (MPC) is a powerful feedback technique that is often used in data-driven robotics. The performance of data-driven MPC depends on the accuracy of the model, which often requires careful tuning. Furthermore, specifying the task with an objective function and synthesizing a feedback policy are not straightforward and typically lead to suboptimal solutions driven by trial and error. To address these challenges, we present a method to jointly optimize the data-driven system identification, task specification, and control synthesis of unknown dynamical systems. We use our method to develop AutoMPC3, a software package designed to automate and optimize data-driven MPC. Empirical evaluation on the pendulum swing-up, cart-pole swing-up, and half-cheetah running demonstrates that our method finds data-driven control policies that outperform offline reinforcement learning, without any hand-tuning.

In the article, we present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem. The challenge of obtaining the gradient of the timing variables is solved by sensitivity analysis of parametric NLPs. The exact analytic gradient is computed from the dual solution as a by-product, whereas existing finite-difference techniques require additional optimization. The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an UAV. Numerical experiments demonstrate that bilevel optimization converges significantly more reliably than a standard NLP solver, and analytical gradients outperform finite differences in terms of computation speed and accuracy. Physical experiments demonstrate its real-time applicability for reactive target tracking tasks.

Time-optimal trajectories for dynamic robotic vehicles are difficult to compute even for state-of-the-art nonlinear programming (NLP) solvers, due to nonlinearity and bang-bang control structure. This paper presents a bilevel optimization framework that addresses these problems by decomposing the spatial and temporal variables into a hierarchical optimization. Specifically, the original problem is divided into an inner layer, which computes a time-optimal velocity profile along a given geometric path, and an outer layer, which refines the geometric path by a Quasi-Newton method. The inner optimization is convex and efficiently solved by interior-point methods. The gradients of the outer layer can be analytically obtained using sensitivity analysis of parametric optimization problems. A novel contribution is to introduce a duality gap in the inner optimization rather than solving it to optimality; this lets the optimizer realize warm-starting of the interior-point method, avoids non-smoothness of the outer cost function caused by active inequality constraint switching. Like prior bilevel frameworks, this method is guaranteed to return a feasible solution at any time, but converges faster than gap-free bilevel optimization. Numerical experiments on a drone model with velocity and acceleration limits show that the proposed method performs faster and more robustly than gap-free bilevel optimization and general NLP solvers.

Robotic automation has the potential to assist human surgeons in performing suturing tasks in microsurgery, and in order to do so a robot must be able to guide a needle with sub-millimeter precision through soft tissue. This paper presents a robotic suturing system that uses 3D optical coherence tomography (OCT) system for imaging feedback. Calibration of the robot-OCT and robot-needle transforms, wound detection, keypoint identification, and path planning are all performed automatically. The calibration method handles pose uncertainty when the needle is grasped using a variant of iterative closest points. The path planner uses the identified wound shape to calculate needle entry and exit points to yield an evenly-matched wound shape after closure. Experiments on tissue phantoms and animal tissue demonstrate that the system can pass a suture needle through wounds with 0.200 mm overall accuracy in achieving the planned entry and exit points, and over 20× more precise than prior autonomous suturing robots.

This paper proposes a machine learning method to predict the solutions of related nonlinear optimal control problems given some parametric input, such as the initial state. The map between problem parameters to optimal solutions is called the problem-optimum map, and is often discontinuous due to nonconvexity, discrete homotopy classes, and control switching. This causes difficulties for traditional function approximators such as neural networks, which assume continuity of the underlying function. This paper proposes a mixture of experts (MoE) model composed of a classifier and several regressors, where each regressor is tuned to a particular continuous region. A novel training approach is proposed that trains classifier and regressors independently. MoE greatly outperforms standard neural networks, and achieves highly reliable trajectory prediction (over 99.5% accuracy) in several dynamic vehicle control problems.

This paper presents a general framework to find time-optimal trajectories for dynamic vehicles like drones and autonomous cars. Hindered by its nonlinear objective and complex constraints, this problem is hard even for state-of the-art nonlinear programming (NLP) solvers. The proposed framework addresses the problem by bilevel optimization. Specifically, the original problem is divided into an inner layer, which computes a time-optimal velocity profile along a fixed geometric path, and an outer layer, which refines the geometric path by a Quasi-Newton method. The inner optimization is convex and efficiently solved by interior-point methods. A novel variable reordering method is introduced to accelerate the optimization of the velocity profile. The gradients of the outer layer can be derived from the Lagrange multipliers using sensitivity analysis of parametric optimization problems. The method is guaranteed to return a feasible solution at any time, and numerical experiments on a ground vehicle with friction circle dynamics model show that the proposed method performs more robustly than general NLP solvers.

Deep anterior lamellar keratoplasty (DALK) is a promising technique for corneal transplantation that avoids the chronic immunosuppression comorbidities and graft rejection risk associated with penetrating keratoplasty (PKP), the standard procedure. In DALK, surgeons must insert a needle 90% through the 500 μm cornea without penetrating its underlying membrane. This pushes surgeons to their manipulation and visualization limits such that 59% of DALK attempts fail due to corneal perforation or inadequate needle depth. We propose a robot-assisted solution to jointly solve the manipulation and visualization challenges using a cooperatively-controlled, precise robot arm and live optical coherence tomography (OCT) imaging, respectively. Our system features an interface handle, with which the surgeon and robot cooperatively hold the tool, and a posterior corneal boundary virtual fixture driven by real-time OCT segmentation. A study in which three operators performed DALK needle insertions manually and cooperatively in ex vivo human corneas demonstrated an 84% improvement in perforation-free needle depth without an increased perforation rate.

Nonlinear optimal control problems are challenging to solve efficiently due to non-convexity. This paper introduces a trajectory optimization approach that achieves realtime performance by combining machine learning to predict optimal trajectories with refinement by quadratic optimization. First, a library of optimal trajectories is calculated offline and used to train a neural network. Online, the neural network predicts a trajectory for a novel initial state and cost function, and this prediction is further optimized by a sparse quadratic programming solver. We apply this approach to a fly-to-target movement problem for an indoor quadrotor. Experiments demonstrate that the technique calculates near-optimal trajectories in a few milliseconds, and generates agile movement that can be tracked more accurately than existing methods.

Nonlinear optimal control problems are challenging to solve due to the prevalence of local minima that prevent convergence and/or optimality. This paper describes nearest-neighbors optimal control (NNOC), a data-driven framework for nonlinear optimal control using indirect methods. It determines initial guesses for new problems with the help of precomputed solutions to similar problems, retrieved using k-nearest neighbors. A sensitivity analysis technique is introduced to linearly approximate the variation of solutions between new and precomputed problems based on their variation of parameters. Experiments show that NNOC can obtain the global optimal solution orders of magnitude faster than standard random restart methods, and sensitivity analysis can further reduce the solving time almost by half. Examples are shown on two optimal control problems in vehicle control.