Non-Gaussian belief space planning: Correctness and complexity

Platt, Robert; Kaelbling, Leslie Pack; Lozano-Pérez, Tomás; Tedrake, Russ

doi:10.1109/icra.2012.6225223

Cited by 19 publications

(20 citation statements)

References 10 publications

(12 reference statements)

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“…In this section, we test the proposed approach on a popular problem known as "light-dark domain" [16] which has been previously solved using techniques like belief-space planner [16] and convex optimization [17]. In this problem, a robot with noisy dynamics has to localize its position before entering a pre-defined goal region to obtain reward.…”

Section: B Light-dark Domainmentioning

confidence: 99%

“…There are regions in the state-space with beacons, i.e., light regions where highly accurate observations can be obtained while all other parts of the state-space are dark regions with large observation noise. Let the system be, Note that our formulation is non-convex and is a harder problem than a quadratic gradient in G(x) considered in [16], [17]. A gradient ensures that even greedy policies can solve the problem whereas in our case, SARSOP is not aware of any good policy until it explicitly samples the light region.…”

Section: B Light-dark Domainmentioning

confidence: 99%

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Sampling-based algorithms for continuous-time POMDPs

Chaudhari

Karaman

Hsu

2013

2013 American Control Conference

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Abstract-This paper focuses on a continuous-time, continuous-space formulation of the stochastic optimal control problem with nonlinear dynamics and observation noise. We lay the mathematical foundations to construct, via incremental sampling, an approximating sequence of discretetime finite-state partially observable Markov decision processes (POMDPs), such that the behavior of successive approximations converges to the behavior of the original continuous system in an appropriate sense. We also show that the optimal cost function and control policies for these POMDP approximations converge almost surely to their counterparts for the underlying continuous system in the limit. We demonstrate this approach on two popular continuous-time problems, viz., the LinearQuadratic-Gaussian (LQG) control problem and the light-dark domain problem.

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Section: B Light-dark Domainmentioning

confidence: 99%

Section: B Light-dark Domainmentioning

confidence: 99%

Sampling-based algorithms for continuous-time POMDPs

Chaudhari

Karaman

Hsu

2013

2013 American Control Conference

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“…Our work instead builds on the approach of Platt et al [13], [14]. That work plans a sequence of actions that will generate observations that distinguish a hypothesised state from competing hypotheses while also reaching a goal position.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to [13], our approach encodes information gathering actions to localise an object to be grasped in 6 dimensions while simultaneously attempts to achieve the task. Similarly to [13], [14], our method is guaranteed to converge to the true state of the system in which a reach-to-grasp trajectory suceeds with high probability. Here we also show how this approach can be extended to planning the motion of a manipulator performing multi-finger grasping.…”

Section: Introductionmentioning

confidence: 99%

Sequential trajectory re-planning with tactile information gain for dexterous grasping under object-pose uncertainty

Zito

Kopicki

Stolkin

et al. 2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Dexterous grasping of objects with uncertain pose is a hard unsolved problem in robotics. This paper solves this problem using information gain re-planning. First we show how tactile information, acquired during a failed attempt to grasp an object can be used to refine the estimate of that object's pose. Second, we show how this information can be used to replan new reach to grasp trajectories for successive grasp attempts. Finally we show how reach-to-grasp trajectories can be modified, so that they maximise the expected tactile information gain, while simultaneously delivering the hand to the grasp configuration that is most likely to succeed. Our main novel outcome is thus to enable tactile information gain planning for Dexterous, high degree of freedom (DoFs) manipulators. We achieve this using a combination of information gain planning, hierarchical probabilistic roadmap planning, and belief updating from tactile sensors for objects with nonGaussian pose uncertainty in 6 dimensions. The method is demonstrated in trials with simulated robots. Sequential replanning is shown to achieve a greater success rate than single grasp attempts, and trajectories that maximise information gain require fewer re-planning iterations than conventional planning methods before a grasp is achieved.

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“…Similarly, other approaches for belief space planning [24] [84] for an exception to this) for computational efficiency and hence the true belief state is not tracked.…”

Section: Planning Under Uncertaintymentioning

confidence: 99%

Funnel libraries for real-time robust feedback motion planning

Majumdar

Tedrake

2017

The International Journal of Robotics Research

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321

270

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We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real-time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of "funnels" along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances.We demonstrate and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (∼12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, the resulting hardware demonstrations on a fixed-wing airplane constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in realtime in environments with complex geometric constraints.The key computational engine we leverage is sums-of-squares (SOS) programming. While SOS programming allows us to apply our approach to systems of relatively high dimensionality (up to approximately 10-15 dimensional state spaces), scaling our approach to higher dimensional systems such as humanoid robots requires a different set of computational tools. In this thesis, we demonstrate how DSOS and SDSOS programming, which are recently introduced alternatives to SOS programming, can be employed to achieve this improved scalability and handle control systems with as many as 30-50 state dimensions. My conversations with him on measure theory, functional analysis, and algebraic topology were extremely enriching and provided me with a set of technical tools that will no doubt be very valuable going forwards. I am grateful to Hongkai for giving me the chance to explore problems in grasping and manipulation with him. Hongkai's incredible capacity to work long hours have been an inspiration throughout my time as a graduate student and have pushed me to work that extra bit longer myself. I have lost count of the number of times a quick late night conversation with him has helped solve a problem that I was stuck on.I would also like to thank the other members of the Robot Locomotion Group for inspiration, advice, help, and entertainment during my time here. It has been an honor to work with people who will no doubt lead our field in years to come. Ian Manchester, Zack Jackowski, Michael Levashov, John Roberts,...

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Non-Gaussian belief space planning: Correctness and complexity

Cited by 19 publications

References 10 publications

Sampling-based algorithms for continuous-time POMDPs

Sampling-based algorithms for continuous-time POMDPs

Sequential trajectory re-planning with tactile information gain for dexterous grasping under object-pose uncertainty

Funnel libraries for real-time robust feedback motion planning

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