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Robot Locomotion Group
The Robot Locomotion Group is a part of Robotics @ MIT and CSAIL.
Locomotion Group Paper and Multimedia News
This paper presents a novel method, combining new formulations and sampling, to improve the scalability of sumofsquares (SOS) programsbased system verification. Regionofattraction approximation problems are considered for polynomial, polynomial with generalized LurÂ’e uncertainty, and rational trigonometric multirigidbody systems. Our method starts by identifying that Lagrange multipliers, traditionally heavily used for Sprocedures, are a major culprit of creating bloated SOS programs. In light of this, we exploit inherent system properties such as continuity, convexity, and implicit algebraic structure, and reformulate the problems as quotientring SOS programs, thereby eliminating all the multipliers. These new programs are smaller, sparser, less constrained, yet less conservative. Their computation is further improved by leveraging a recent result on sampling algebraic varieties. Remarkably, solution correctness is guaranteed with just a finite (in practice, very small) number of samples. Altogether, the proposed method can verify systems well beyond the reach of existing SOSbased approaches (29 states); on smaller problems where a baseline is available, it computes tighter solution 23 orders faster. Source code is included. Under review. Comments welcome. The Surprising Effectiveness of Linear Models for Visual Foresight in Object Pile Manipulation
In this paper, we tackle the problem of pushing piles of small objects into a desired target set using visual feedback. Unlike conventional singleobject manipulation pipelines, which estimate the state of the system parametrized by pose, the underlying physical state of this system is difficult to observe from images. Thus, we take the approach of reasoning directly in the space of images, and acquire the dynamics of visual measurements in order to synthesize a visualfeedback policy. We present a simple controller using an imagespace Lyapunov function, and evaluate the closedloop performance using three different class of models for image prediction: deeplearningbased models for imagetoimage translation, an objectcentric model obtained from treating each pixel as a particle, and a switchedlinear system where an actiondependent linear map is used. Through results in simulation and experiment, we show that for this task, a linear model works surprisingly well  achieving better prediction error, downstream task performance, and generalization to new environments than the deep models we trained on the same amount of data. We believe these results provide an interesting example in the spectrum of models that are most useful for visionbased feedback in manipulation, considering both the quality of visual prediction, as well as compatibility with rigorous methods for control design and analysis. Supplemental materials: https://www.youtube.com/watch?v=HfFSnsnR590 Under review. Comments welcome. Robust Output Feedback Control with Guaranteed Constraint Satisfaction
We propose a method to control linear timevarying (LTV) discretetime systems subject to bounded process disturbances and measurable outputs with bounded noise, and polyhedral constraints over system inputs and states. We search over control policies that map the history of measurable outputs to the current control input. We solve the problem in two stages. First, using the original system, we build a linear system that predicts future observations using the past observations. The bounded errors are characterized using zonotopes. Next, we propose control laws based on affine maps of such output prediction errors, and show that controllers can be synthesized using convex linear/quadratic programs. Furthermore, we can add constraints on trajectories and guarantee their satisfaction for all allowable sequences of observation noise and process disturbances. Our method does not require any assumptions about system controllability and observability. The controller design does not directly take into account the statespace dynamics, and its implementation does not require an observer. Instead, partial observability is often sufficient to design a correct controller. We provide the polytopic representation of observability errors and reachable sets in the form of zonotopes. Illustrative examples are included. To Appear at HSCC 2020. Comments welcome. Warm Start of MixedInteger Programs for Model Predictive Control of Hybrid Systems
In hybrid Model Predictive Control (MPC), a MixedInteger Convex Program (MICP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect consecutive problem instances to be nearly identical. This paper addresses the question of how computations performed at one time step can be reused to accelerate ('warm start') the solution of subsequent MICPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branchandbound algorithm allows an efficient reuse of its search tree and the dual bounds of its leaf nodes. In this paper we extend these ideas to the recedinghorizon settings of MPC. The warmstart algorithm we propose copes naturally with arbitrary model errors, has negligible computational cost, and frequently enables an apriori pruning of most of the search space. Theoretical considerations and experimental evidence show that the proposed method tends to reduce the combinatorial complexity of the hybrid MPC problem to that of a onestep lookahead optimization, greatly easing the online computation burden. Supplemental materials: http://arxiv.org/abs/1910.08251 Under review (arXiv available). Comments welcome. The Nearest Polytope Problem: Algorithms and Application to Controlling Hybrid Systems
We present three algorithms for solving the nearest polytope problem: given a list of polytopes and a distance metric in Euclidean space, find the nearest polytope to a query point. We consider the AHpolytope representation, which generalizes the Hpolytope representation and is particularly useful in the context of control. Through preprocessing the polytopes into efficient data structures, we avoid exhaustive search at query time. We discuss the properties of the algorithms and compare their performances using polytopic datasets motivated by control applications, including samplingbased motion planning and model predictive control. Under review. Comments welcome.
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