Motion Planning with Complex Goals

Bhatia, Amit; Maly, Matthew R.; Kavraki, Lydia E.; Vardi, Moshe Y.

doi:10.1109/mra.2011.942115

Cited by 107 publications

(91 citation statements)

References 63 publications

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“…This abstraction can informally be viewed as a labeled graph that represents possible behaviors of the system. Approximate finite abstractions can be computed using either sampling-based methods (e.g., RRTs) [7,15,18] or reachability-based approaches [2,4,11,17,28].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control of Nonlinear Systems with Temporal Logic Specifications

Wolff

Murray

2016

Springer Tracts in Advanced Robotics

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We present a mathematical programming-based method for optimal control of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite-and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite abstraction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10+ continuous state) systems.

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Section: Introductionmentioning

confidence: 99%

“…Given a finite abstraction of a dynamical system and an LTL specification, controllers can be automatically constructed using an automata-based approach [3,7,10,15,17]. This approach first transforms the LTL formula into an equivalent Büchi automaton whose size may be exponential in the length of the formula [3].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Nonlinear Systems with Temporal Logic Specifications

Wolff

Murray

2016

Springer Tracts in Advanced Robotics

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“…High-level specifications using temporal logics have been employed to improve the expressiveness of a motion planning task (e.g., [3][4][5][6][7][8][9][10]). These logics allow for a natural encoding of both Boolean and temporal constraints, and the classic motion planning task of move from start to goal without collision can be greatly enhanced using these operators.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in the warehouse scenario described above, complex tasks such as "Pick up items from locations A, B, and C, in any order, and drop them off at location D" or "Pick up items from locations A or B and then C and drop them off in D; meanwhile, if B is ever visited, then avoid E" are easily encoded using only temporal and Boolean operators. Given a motion planning specification in the form of a temporal logic formula, existing frameworks (e.g., [3][4][5][6][7][8][9][10]) consider a mixed discrete and continuous approach, where Boolean propositions are mapped to discrete regions of the state space and planning is performed in the continuous space to satisfy the specification.…”

Section: Introductionmentioning

confidence: 99%

Asymptotically Optimal Stochastic Motion Planning with Temporal Goals

Luna

Lahijanian

Moll

et al. 2015

Springer Tracts in Advanced Robotics

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Abstract. This work presents a planning framework that allows a robot with stochastic action uncertainty to achieve a high-level task given in the form of a temporal logic formula. The objective is to quickly compute a feedback control policy to satisfy the task specification with maximum probability. A top-down framework is proposed that abstracts the motion of a continuous stochastic system to a discrete, boundedparameter Markov decision process (bmdp), and then computes a control policy over the product of the bmdp abstraction and a dfa representing the temporal logic specification. Analysis of the framework reveals that as the resolution of the bmdp abstraction becomes finer, the policy obtained converges to optimal. Simulations show that high-quality policies to satisfy complex temporal logic specifications can be obtained in seconds, orders of magnitude faster than existing methods.

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“…In contrast, we motion plan anew each run, but efficiently update scene data structures to handle object interaction. The Synergistic Framework [65] and related methods [4,5,36] are similar to our proposed approach, but there are important differences in the underlying algorithms that suggest these methods may be complementary. The Synergistic Framework finds task plans through forward search, while we use constraint-based methods to efficiently generate task plans.…”

Section: Task and Motion Planningmentioning

confidence: 93%

Incremental Task and Motion Planning: A Constraint-Based Approach

Dantam¹,

Kingston²,

Chaudhuri³

et al.

Robotics: Science and Systems XII

149

115

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Abstract-We present a new algorithm for task and motion planning (TMP) and discuss the requirements and abstractions necessary to obtain robust solutions for TMP in general. Our Iteratively Deepened Task and Motion Planning (IDTMP) method is probabilistically-complete and offers improved performance and generality compared to a similar, state-of-theart, probabilistically-complete planner. The key idea of IDTMP is to leverage incremental constraint solving to efficiently add and remove constraints on motion feasibility at the task level. We validate IDTMP on a physical manipulator and evaluate scalability on scenarios with many objects and long plans, showing order-of-magnitude gains compared to the benchmark planner and a four-times self-comparison speedup from our extensions. Finally, in addition to describing a new method for TMP and its implementation on a physical robot, we also put forward requirements and abstractions for the development of similar planners in the future.

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Motion Planning with Complex Goals

Cited by 107 publications

References 63 publications

Optimal Control of Nonlinear Systems with Temporal Logic Specifications

Optimal Control of Nonlinear Systems with Temporal Logic Specifications

Asymptotically Optimal Stochastic Motion Planning with Temporal Goals

Incremental Task and Motion Planning: A Constraint-Based Approach

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