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1. Manipulating deformable objects by interleaving prediction, planning, and control

   https://doi.org/10.1177/0278364920918299  

   McConachie, Dale ; Dobson, Andrew ; Ruan, Mengyao ; Berenson, Dmitry ( July 2020 , The International Journal of Robotics Research)

   We present a framework for deformable object manipulation that interleaves planning and control, enabling complex manipulation tasks without relying on high-fidelity modeling or simulation. The key question we address is when should we use planning and when should we use control to achieve the task? Planners are designed to find paths through complex configuration spaces, but for highly underactuated systems, such as deformable objects, achieving a specific configuration is very difficult even with high-fidelity models. Conversely, controllers can be designed to achieve specific configurations, but they can be trapped in undesirable local minima owing to obstacles. Our approach consists of three components: (1) a global motion planner to generate gross motion of the deformable object; (2) a local controller for refinement of the configuration of the deformable object; and (3) a novel deadlock prediction algorithm to determine when to use planning versus control. By separating planning from control we are able to use different representations of the deformable object, reducing overall complexity and enabling efficient computation of motion. We provide a detailed proof of probabilistic completeness for our planner, which is valid despite the fact that our system is underactuated and we do not have a steering function. We thenmore »demonstrate that our framework is able to successfully perform several manipulation tasks with rope and cloth in simulation, which cannot be performed using either our controller or planner alone. These experiments suggest that our planner can generate paths efficiently, taking under a second on average to find a feasible path in three out of four scenarios. We also show that our framework is effective on a 16-degree-of-freedom physical robot, where reachability and dual-arm constraints make the planning more difficult.« less
2. Robot-Assisted Pedestrian Regulation Based on Deep Reinforcement Learning

   https://doi.org/10.1109/TCYB.2018.2878977  

   Wan, Zhiqiang ; Jiang, Chao ; Fahad, Muhammad ; Ni, Zhen ; Guo, Yi ; He, Haibo ( January 2019 , IEEE Transactions on Cybernetics)

   Pedestrian regulation can prevent crowd accidents and improve crowd safety in densely populated areas. Recent studies use mobile robots to regulate pedestrian flows for desired collective motion through the effect of passive human-robot interaction (HRI). This paper formulates a robot motion planning problem for the optimization of two merging pedestrian flows moving through a bottleneck exit. To address the challenge of feature representation of complex human motion dynamics under the effect of HRI, we propose using a deep neural network to model the mapping from the image input of pedestrian environments to the output of robot motion decisions. The robot motion planner is trained end-to-end using a deep reinforcement learning algorithm, which avoids hand-crafted feature detection and extraction, thus improving the learning capability for complex dynamic problems. Our proposed approach is validated in simulated experiments, and its performance is evaluated. The results demonstrate that the robot is able to find optimal motion decisions that maximize the pedestrian outflow in different flow conditions, and the pedestrian-accumulated outflow increases significantly compared to cases without robot regulation and with random robot motion.
3. Smoothed analysis of the low-rank approach for smooth semidefinite programs

   Pumir, Thomas ; Jelassi, Samy ; Boumal, Nicolas ( January 2018 , Neural Information Processing Systems (NIPS))

   We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size nk such that X = Y Y  is the SDP variable. The advantages of such formulation are twofold: the dimension of the optimization variable is reduced, and positive semidefiniteness is naturally enforced. However, optimization in Y is non-convex. In prior work, it has been shown that, when the constraints on the factorized variable regularly define a smooth manifold, provided k is large enough, for almost all cost matrices, all second-order stationary points (SOSPs) are optimal. Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading to the question: are such points also approximately optimal? To answer it, under similar assumptions, we use smoothed analysis to show that approximate SOSPs for a randomly perturbed objective function are approximate global optima, with k scaling like the square root of the number of constraints (up to log factors). Moreover, we bound the optimality gap at the approximate solution of the perturbed problem with respect to the original problem. We particularize our results to anmore »SDP relaxation of phase retrieval.« less
4. Motion Planning around Obstacles with Convex Optimization

   Tobia Marcucci, Mark Petersen2 ( May 2022 , ArXivorg)

   Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulationmore »on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.« less
5. Faster Matchings via Learned Duals

   Dinitz, Michael ; Im, Sungjin ; Lavastida, Thomas ; Moseley, Benjamin ; Vassilvitskii, Sergei ( January 2021 , Advances in neural information processing systems)

   A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in the design of competitive online algorithms. However, the question of improving algorithm running times with predictions has largely been unexplored. We take a first step in this direction by combining the idea of machine-learned predictions with the idea of "warm-starting" primal-dual algorithms. We consider one of the most important primitives in combinatorial optimization: weighted bipartite matching and its generalization to b-matching. We identify three key challenges when using learned dual variables in a primal-dual algorithm. First, predicted duals may be infeasible, so we give an algorithm that efficiently maps predicted infeasible duals to nearby feasible solutions. Second, once the duals are feasible, they may not be optimal, so we show that they can be used to quickly find an optimal solution. Finally, such predictions are useful only if they can be learned, so we show that the problem of learning duals for matching has low sample complexity. We validate our theoretical findings through experiments on both real and synthetic data. As a result we give a rigorous,more »practical, and empirically effective method to compute bipartite matchings.« less