LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

Tedrake, Russ; Manchester, Ian R.; Tobenkin, Mark M.; Roberts, John W.

doi:10.1177/0278364910369189

Cited by 378 publications

(373 citation statements)

References 30 publications

Supporting

Mentioning

372

Contrasting

Order By: Relevance

“…Mason [18] first introduced the concept in the context of performing sensorless manipulation actions that employ passive mechanics to reduce part uncertainty. Later, Burridge et al [3] applied the funnel analogy to feedback control in the form of sequential composition of controllers, spawning much follow-on work [7,8,24]. This body of work is sensor-agnostic in that the type and quality of sensor data is assumed to be homogeneous throughout the configuration space.…”

Section: Sequential Composition Of Sensorsmentioning

confidence: 99%

Towards Coordinated Precision Assembly with Robot Teams

Dogar¹,

Knepper²,

Spielberg³

et al. 2015

Experimental Robotics

View full text Add to dashboard Cite

Abstract. We present a system in which a flexible team of robots coordinate to assemble large, complex, and diverse structures autonomously. Our system operates across a wide range of spatial scales and tolerances, using a hierarchical perception architecture. For the successful execution of very precise assembly operations under initial uncertainty, our system starts with high-field of view but low accuracy sensors, and gradually use low field-of-view but high accuracy sensors. Our system also uses a failure detection and recovery system, integrated with this hierarchical perception architecture: upon losing track of a feature, our system retracts to using high-field of view systems to re-localize. Additionally, we contribute manipulation skills and tools necessary to assemble large structures with high precision. First, the team of robots coordinate to transport large assembly parts which are too heavy for a single robot to carry. Second, we develop a new tool which is capable of co-localizing holes and fasteners for robust insertion and fastening. We present real robot experiments where we measure the contribution of the hierarchical perception and failure recovery approach to the robustness of our system. We also present an extensive set of experiments where our robots successfully insert all 80 of the attempted fastener insertion operations.

show abstract

Section: Sequential Composition Of Sensorsmentioning

confidence: 99%

Towards Coordinated Precision Assembly with Robot Teams

Dogar¹,

Knepper²,

Spielberg³

et al. 2015

Experimental Robotics

View full text Add to dashboard Cite

show abstract

“…avoids obstacles and switches between the planned sequence of funnels). This can be viewed as an extension of the LQR-Trees algorithm [24] for feedback motion planning, which was limited to offline planning due to the relatively large computational cost of computing the funnels; our algorithm is suitable for real-time, online planning. We expect this framework to be useful in robotic tasks where the dynamics and perceptual system of the robot are difficult to model perfectly and for which the robot does not have access to the geometry of the environment till runtime.…”

Section: Contributionsmentioning

confidence: 99%

“…Note that the objective in our sums-of-squares program, ∑ t i ρ(t i ), helps us find a tight conservative estimate of the set of states the closed loop system may evolve to under the given uncertain dynamics. Further, one can very easily augment this optimization program to handle actuator saturations in a manner similar to the one described in [24].…”

Section: Robust Regions Of Finite Time Invariancementioning

confidence: 99%

“…LQR-Trees [24] and the minimum snap trajectory generation approach [16] operate by generating locally optimal trajectories through state space and stabilizing them locally. However, the former approach lacks the ability to handle scenarios in which the task and environment are unknown till runtime since it is too computationally intensive for online implementation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Online Motion Planning with Regions of Finite Time Invariance

Majumdar

Tedrake

2013

Springer Tracts in Advanced Robotics

Self Cite

View full text Add to dashboard Cite

In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to offline planning due to the computational cost of safety verification. Here we take a trajectory library approach by designing controllers that stabilize the nominal trajectories in the library and precomputing regions of finite time invariance ("funnels") for the resulting closed loop system. We leverage sums-of-squares programming in order to efficiently compute funnels which take into account bounded disturbances and uncertainty. 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 our method on a simulation of a plane flying through a two dimensional forest of polygonal trees with parametric uncertainty and disturbances in the form of a bounded "cross-wind".

show abstract

“…Consequently, the development of computationally tractable algorithms for reachability analysis is critical not only for verifying safe system behavior, but also due to its applicability during incremental control design [20]. This paper presents a numerical approach to construct the set of points that reach a given target set at a specified finite time for controlled polynomial hybrid systems.…”

Section: Introductionmentioning

confidence: 99%

Convex computation of the reachable set for controlled polynomial hybrid systems

Shia

Vasudevan

Bajcsy

et al. 2014

53rd IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

Abstract-This paper presents an approach to computing the time-limited backwards reachable set (BRS) of a semialgebraic target set for controlled polynomial hybrid systems with semialgebraic state and input constraints. By relying on the notion of occupation measures, the computation of the BRS of a target set that may be distributed across distinct subsystems of the hybrid system, is posed as an infinite dimensional linear program (LP). Computationally tractable approximations to this LP are constructed via a sequence of semidefinite programs each of which is proven to construct an outer approximation of the true BRS with asymptotically vanishing conservatism. In contrast to traditional Lyapunov based approaches, the presented approach is convex and does not require any form of initialization. The performance of the presented algorithm is illustrated on 2 nonlinear controlled hybrid systems.

show abstract

LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

Cited by 378 publications

References 30 publications

Towards Coordinated Precision Assembly with Robot Teams

Towards Coordinated Precision Assembly with Robot Teams

Robust Online Motion Planning with Regions of Finite Time Invariance

Convex computation of the reachable set for controlled polynomial hybrid systems

Contact Info

Product

Resources

About