Showing papers on "Motion planning published in 2014"

Motion planning with sequential convex optimization and convex collision checking

Abstract: We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http://rll.berkeley.edu/trajopt/ijrr.

Sampling-Based Robot Motion Planning: A Review

Abstract: Motion planning is a fundamental research area in robotics. Sampling-based methods offer an efficient solution for what is otherwise a rather challenging dilemma of path planning. Consequently, these methods have been extended further away from basic robot planning into further difficult scenarios and diverse applications. A comprehensive survey of the growing body of work in sampling-based planning is given here. Simulations are executed to evaluate some of the proposed planners and highlight some of the implementation details that are often left unspecified. An emphasis is placed on contemporary research directions in this field. We address planners that tackle current issues in robotics. For instance, real-life kinodynamic planning, optimal planning, replanning in dynamic environments, and planning under uncertainty are discussed. The aim of this paper is to survey the state of the art in motion planning and to assess selected planners, examine implementation details and above all shed a light on the current challenges in motion planning and the promising approaches that will potentially overcome those problems.

Combined task and motion planning through an extensible planner-independent interface layer

Abstract: The need for combined task and motion planning in robotics is well understood. Solutions to this problem have typically relied on special purpose, integrated implementations of task planning and motion planning algorithms. We propose a new approach that uses off-the-shelf task planners and motion planners and makes no assumptions about their implementation. Doing so enables our approach to directly build on, and benefit from, the vast literature and latest advances in task planning and motion planning. It uses a novel representational abstraction and requires only that failures in computing a motion plan for a high-level action be identifiable and expressible in the form of logical predicates at the task level. We evaluate the approach and illustrate its robustness through a number of experiments using a state-of-the-art robotics simulator and a PR2 robot. These experiments show the system accomplishing a diverse set of challenging tasks such as taking advantage of a tray when laying out a table for dinner and picking objects from cluttered environments where other objects need to be re-arranged before the target object can be reached.

Whole-body motion planning with centroidal dynamics and full kinematics

Abstract: To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full-body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.

Sampling-based robotic information gathering algorithms

Abstract: We propose three sampling-based motion planning algorithms for generating informative mobile robot trajectories. The goal is to find a trajectory that maximizes an information quality metric (e.g. variance reduction, information gain, or mutual information) and also falls within a pre-specified budget constraint (e.g. fuel, energy, or time). Prior algorithms have employed combinatorial optimization techniques to solve these problems, but existing techniques are typically restricted to discrete domains and often scale poorly in the size of the problem. Our proposed rapidly exploring information gathering (RIG) algorithms combine ideas from sampling-based motion planning with branch and bound techniques to achieve efficient information gathering in continuous space with motion constraints. We provide analysis of the asymptotic optimality of our algorithms, and we present several conservative pruning strategies for modular, submodular, and time-varying information objectives. We demonstrate that our proposed techniques find optimal solutions more quickly than existing combinatorial solvers, and we provide a proof-of-concept field implementation on an autonomous surface vehicle performing a wireless signal strength monitoring task in a lake.

FIRM: Sampling-based feedback motion-planning under motion uncertainty and imperfect measurements

Abstract: In this paper we present feedback-based information roadmap (FIRM), a multi-query approach for planning under uncertainty which is a belief-space variant of probabilistic roadmap methods. The crucial feature of FIRM is that the costs associated with the edges are independent of each other, and in this sense it is the first method that generates a graph in belief space that preserves the optimal substructure property. From a practical point of view, FIRM is a robust and reliable planning framework. It is robust since the solution is a feedback and there is no need for expensive replanning. It is reliable because accurate collision probabilities can be computed along the edges. In addition, FIRM is a scalable framework, where the complexity of planning with FIRM is a constant multiplier of the complexity of planning with PRM. In this paper, FIRM is introduced as an abstract framework. As a concrete instantiation of FIRM, we adopt stationary linear quadratic Gaussian (SLQG) controllers as belief stabilizers and introduce the so-called SLQG-FIRM. In SLQG-FIRM we focus on kinematic systems and then extend to dynamical systems by sampling in the equilibrium space. We investigate the performance of SLQG-FIRM in different scenarios.

Reducing the Barrier to Entry of Complex Robotic Software: a MoveIt! Case Study

Abstract: Developing robot agnostic software frameworks involves synthesizing the disparate fields of robotic theory and software engineering while simultaneously accounting for a large variability in hardware designs and control paradigms. As the capabilities of robotic software frameworks increase, the setup difficulty and learning curve for new users also increase. If the entry barriers for configuring and using the software on robots is too high, even the most powerful of frameworks are useless. A growing need exists in robotic software engineering to aid users in getting started with, and customizing, the software framework as necessary for particular robotic applications. In this paper a case study is presented for the best practices found for lowering the barrier of entry in the MoveIt! framework, an open-source tool for mobile manipulation in ROS, that allows users to 1) quickly get basic motion planning functionality with minimal initial setup, 2) automate its configuration and optimization, and 3) easily customize its components. A graphical interface that assists the user in configuring MoveIt! is the cornerstone of our approach, coupled with the use of an existing standardized robot model for input, automatically generated robot-specific configuration files, and a plugin-based architecture for extensibility. These best practices are summarized into a set of barrier to entry design principles applicable to other robotic software. The approaches for lowering the entry barrier are evaluated by usage statistics, a user survey, and compared against our design objectives for their effectiveness to users.

Towards Reliable Grasping and Manipulation in Household Environments

Abstract: We present a complete software architecture for reliable grasping of household objects. Our work combines aspects such as scene interpretation from 3D range data, grasp planning, motion planning, and grasp failure identification and recovery using tactile sensors. We build upon, and add several new contributions to the significant prior work in these areas. A salient feature of our work is the tight coupling between perception (both visual and tactile) and manipulation, aiming to address the uncertainty due to sensor and execution errors. This integration effort has revealed new challenges, some of which can be addressed through system and software engineering, and some of which present opportunities for future research. Our approach is aimed at typical indoor environments, and is validated by long running experiments where the PR2 robotic platform was able to consistently grasp a large variety of known and unknown objects. The set of tools and algorithms for object grasping presented here have been integrated into the open-source Robot Operating System (ROS).

Layered costmaps for context-sensitive navigation.

Abstract: Many navigation systems, including the ubiquitous ROS navigation stack, perform path-planning on a single costmap, in which the majority of information is stored in a single grid. This approach is quite successful at generating collision-free paths of minimal length, but it can struggle in dynamic, people-filled environments when the values in the costmap expand beyond occupied or free space. We have created and implemented a new method called layered costmaps, which work by separating the processing of costmap data into semantically-separated layers. Each layer tracks one type of obstacle or constraint, and then modifies a master costmap which is used for the path planning. We show how the algorithm can be integrated with the open-source ROS navigation stack, and how our approach is easier to fine-tune to specific environmental contexts than the existing monolithic one. Our design also results in faster path planning in practical use, and exhibits a cleaner separation of concerns that the original architecture. The new algorithm also makes it possible to represent complex cost values in order to create navigation behavior for a wide range of contexts.

A constraint-based method for solving sequential manipulation planning problems

Abstract: In this paper, we describe a strategy for integrated task and motion planning based on performing a symbolic search for a sequence of high-level operations, such as pick, move and place, while postponing geometric decisions. Partial plans (skeletons) in this search thus pose a geometric constraintsatisfaction problem (CSP), involving sequences of placements and paths for the robot, and grasps and locations of objects. We propose a formulation for these problems in a discretized configuration space for the robot. The resulting problems can be solved using existing methods for discrete CSP.

Modelling of Mechanical and Mechatronic Systems MMaMS 2014 Path planning with modified A star algorithm for a mobile robot

Abstract: This article deals with path planning of a mobile robot based on a grid map. Essential assumption for path planning is a mobile robot with functional and reliable reactive navigation and SLAM. Therefore, such issues are not addressed in this article. The main body of the article introduces several modifications (Basic Theta*, Phi*) and improvements (RSR, JPS) of A star algorithm. These modifications are focused primarily on computational time and the path optimality. Individual modifications were evaluated in several scenarios, which varied in the complexity of environment. On the basis of these evaluations, it is possible to choose path planning method suitable for individual scenario. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the Modelling of Mechanical and Mechatronic Systems MMaMS 2014. Keywords: path planning, A* algorithm, Basic Theta*, Phi*, Jump Point Search Nomenclature SLAM Simultaneous Localization and Mapping A* A star RSR Rectangular Symmetry Reduction JPS Jump Point Search

A Robotic Crack Inspection and Mapping System for Bridge Deck Maintenance

Abstract: One of the important tasks for bridge maintenance is bridge deck crack inspection. Traditionally, a human inspector detects cracks using his/her eyes and marks the location of cracks manually. However, the accuracy of the inspection result is low due to the subjective nature of human judgement. We propose a crack inspection system that uses a camera-equipped mobile robot to collect images on the bridge deck. In this method, the Laplacian of Gaussian (LoG) algorithm is used to detect cracks and a global crack map is obtained through camera calibration and robot localization. To ensure that the robot collects all the images on the bridge deck, a path planning algorithm based on the genetic algorithm is developed. The path planning algorithm finds a solution which minimizes the number of turns and the traveling distance. We validate our proposed system through both simulations and experiments.

Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning

Abstract: Nonholonomic systems are control systems which depend linearly on the control Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems

A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm

Abstract: Finding the time-optimal parameterization of a given path subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this paper is to provide a general, fast, and robust implementation of this component. For this, we give a complete solution to the issue of dynamic singularities, which are the main cause of failure in existing implementations. We then present an open-source implementation of the algorithm in C++/Python and demonstrate its robustness and speed in various robotics settings.

A literature review of UAV 3D path planning

Abstract: 3D path planning of unmanned aerial vehicle (UAV) targets at finding an optimal and collision free path in a 3D cluttered environment while taking into account the geometric, physical and temporal constraints. Although a lot of works have been done to solve UAV 3D path planning problem, there lacks a comprehensive survey on this topic, let alone the recently published works that focus on this field. This paper analyses the most successful UAV 3D path planning algorithms that developed in recent years. This paper classifies the UAV 3D path planning methods into five categories, sampling-based algorithms, node-based algorithms, mathematical model based algorithms, Bio-inspired algorithms, and multi-fusion based algorithms. For each category a critical analysis and comparison is given. Furthermore a comprehensive applicable analysis for each kind of method is presented after considering its working mechanism and time complexity.

Automated composition of motion primitives for multi-robot systems from safe LTL specifications

Abstract: Author(s): Saha, I; Ramaithitima, R; Kumar, V; Pappas, GJ; Seshia, SA | Abstract: We present a compositional motion planning framework for multi-robot systems based on an encoding to satisfiability modulo theories (SMT). In our framework, the desired behavior of a group of robots is specified using a set of safe linear temporal logic (LTL) properties. Our method relies on a library of motion primitives, each of which corresponds to a controller that ensures a particular trajectory in a given configuration. Using the closed-loop behavior of the robots under the action of different controllers, we formulate the motion planning problem as an SMT solving problem and use an off-the-shelf SMT solver to generate trajectories for the robots. Our approach can also be extended to synthesize optimal cost trajectories where optimality is defined with respect to the available motion primitives. Experimental results show that our framework can efficiently solve complex motion planning problems in the context of multi-robot systems.

Minimizing Energy Consumption of Wheeled Mobile Robots via Optimal Motion Planning

Abstract: This paper presents a new optimal motion planning aiming to minimize the energy consumption of a wheeled mobile robot in robot applications. A model that can be used to formulate the energy consumption for kinetic energy transformation and for overcoming traction resistance is developed first. This model will provide a base for minimizing the robot energy consumption through a proper motion planning. To design the robot path, the A* algorithm is employed to generate an energy-efficient path where a new energy-related criterion is utilized in the cost function. To achieve a smooth trajectory along the generated path, the appropriate arrival time and velocity at the defined waypoints are selected for minimum energy consumption. Simulations and experiments are performed to demonstrate the energy-saving efficiency of the proposed motion planning approach.

Finding a Needle in an Exponential Haystack: Discrete RRT for Exploration of Implicit Roadmaps in Multi-robot Motion Planning.

Abstract: We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.

Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints

Abstract: We consider a reach-avoid differential game, in which one of the players aims to steer the system into a target set without violating a set of state constraints, while the other player tries to prevent the first from succeeding; the system dynamics, target set, and state constraints may all be time-varying. The analysis of this problem plays an important role in collision avoidance, motion planning and aircraft control, among other applications. Previous methods for computing the guaranteed winning initial conditions and strategies for each player have either required augmenting the state vector to include time, or have been limited to problems with either no state constraints or entirely static targets, constraints and dynamics. To incorporate time-varying dynamics, targets and constraints without the need for state augmentation, we propose a modified Hamilton-Jacobi-Isaacs equation in the form of a double-obstacle variational inequality, and prove that the zero sublevel set of its viscosity solution characterizes the capture basin for the target under the state constraints. Through this formulation, our method can compute the capture basin and winning strategies for time-varying games at no additional computational cost with respect to the time-invariant case. We provide an implementation of this method based on well-known numerical schemes and show its convergence through a simple example; we include a second example in which our method substantially outperforms the state augmentation approach.

Superior Path Planning Mechanism for Mobile Beacon-Assisted Localization in Wireless Sensor Networks

Abstract: In many wireless sensor network applications, such as warning systems or healthcare services, it is necessary to update the captured data with location information. A promising solution for statically deployed sensors is to benefit from mobile beacon-assisted localization. The main challenge is to design and develop an optimum path planning mechanism for a mobile beacon to decrease the required time for determining location, increase the accuracy of the estimated position, and increase the coverage. In this paper, we propose a novel superior path planning mechanism called Z-curve. Our proposed trajectory can successfully localize all deployed sensors with high precision and the shortest required time for localization. We also introduce critical metrics, including the ineffective position rate for further evaluation of mobile beacon trajectories. In addition, we consider an accurate and reliable channel model, which helps to provide more realistic evaluation. Z-curve is compared with five existing path planning schemes based on three different localization techniques such as weighted centroid localization and trilateration with time priority and accuracy priority. Furthermore, the performance of the Z-curve is evaluated at the presence of obstacles and Z-curve obstacle-handling trajectory is proposed to mitigate the obstacle problem on localization. Simulation results show the advantages of our proposed path planning scheme over the existing schemes.

Optimal motion planning for overhead cranes

Abstract: Overhead cranes are widely used in industrial applications for material displacing. Many linear or non-linear control schemes have been proposed for overhead cranes and implemented on electronic systems, but energy efficiency of transportation has seldom been considered in motion planning. This study aims at finding an optimal solution of motion planning in terms of energy efficiency for overhead cranes. Using the optimal control method an optimal trajectory is obtained with less energy consumption than the compared trajectories and is also satisfying physical and practical constraints such as swing, acceleration and jerk. Besides the energy optimal model, the authors also propose two other models to optimise time efficiency and safety during transportation. The results obtained have been compared with some existing motion trajectories, and have been shown to be superior to these benchmarks in terms of energy efficiency, time efficiency and safety, respectively.

Long-term 3D map maintenance in dynamic environments

Abstract: New applications of mobile robotics in dynamic urban areas require more than the single-session geometric maps that have dominated simultaneous localization and mapping (SLAM) research to date; maps must be updated as the environment changes and include a semantic layer (such as road network information) to aid motion planning in dynamic environments. We present an algorithm for long-term localization and mapping in real time using a three-dimensional (3D) laser scanner. The system infers the static or dynamic state of each 3D point in the environment based on repeated observations. The velocity of each dynamic point is estimated without requiring object models or explicit clustering of the points. At any time, the system is able to produce a most-likely representation of underlying static scene geometry. By storing the time history of velocities, we can infer the dominant motion patterns within the map. The result is an online mapping and localization system specifically designed to enable long-term autonomy within highly dynamic environments. We validate the approach using data collected around the campus of ETH Zurich over seven months and several kilometers of navigation. To the best of our knowledge, this is the first work to unify long-term map update with tracking of dynamic objects.

Bayesian Optimisation for informative continuous path planning.

Abstract: Environmental monitoring with mobile robots requires solving the informative path planning problem. A key challenge is how to compute a continuous path over space and time that will allow a robot to best sample the environment for an initially unknown phenomenon. To address this problem we devise a layered Bayesian Optimisation approach that uses two Gaussian Processes, one to model the phenomenon and the other to model the quality of selected paths. By using different acquisition functions over both models we tackle the exploration-exploitation trade off in a principled manner. Our method optimises sampling over continuous paths and allows us to find trajectories that maximise the reward over the path. We test our method on a large scale experiment for modelling ozone concentration in the US, and on a mobile robot modelling the changes in luminosity. Comparisons are presented against information based criteria and point-based strategies demonstrating the benefits of our method.

Toward image based visual servoing for aerial grasping and perching

Abstract: This paper addresses the dynamics, control, planning, and visual servoing for micro aerial vehicles to perform high-speed aerial grasping tasks. We draw inspiration from agile, fast-moving birds, such as raptors, that detect, locate, and execute high-speed swoop maneuvers to capture prey. Since these grasping maneuvers are predominantly in the sagittal plane, we consider the planar system and present mathematical models and algorithms for motion planning and control, required to incorporate similar capabilities in quadrotors equipped with a monocular camera. In particular, we develop a dynamical model directly in the image space, show that this is a differentially-flat system with the image features serving as flat outputs, outline a method for generating trajectories directly in the image feature space, develop a geometric visual controller that considers the second order dynamics (in contrast to most visual servoing controllers that assume first order dynamics), and present validation of our methods through both simulations and experiments.

Sampling-based A* algorithm for robot path-planning

Abstract: This paper presents a generalization of the classic A* algorithm to the domain of sampling-based motion planning. The root assumptions of the A* algorithm are examined and reformulated in a manner that enables a direct use of the search strategy as the driving force behind the generation of new samples in a motion graph. Formal analysis is presented to show probabilistic completeness and convergence of the method. This leads to a highly exploitative method which does not sacrifice entropy. Many improvements are presented to this versatile method, most notably, an optimal connection strategy, a bias towards the goal region via an Anytime A* heuristic, and balancing of exploration and exploitation on a simulated annealing schedule. Empirical results are presented to assess the proposed method both qualitatively and quantitatively in the context of high-dimensional planning problems. The potential of the proposed methods is apparent, both in terms of reliability and quality of solutions found.

Motion planning under uncertainty for on-road autonomous driving

Abstract: We present a motion planning framework for autonomous on-road driving considering both the uncertainty caused by an autonomous vehicle and other traffic participants. The future motion of traffic participants is predicted using a local planner, and the uncertainty along the predicted trajectory is computed based on Gaussian propagation. For the autonomous vehicle, the uncertainty from localization and control is estimated based on a Linear-Quadratic Gaussian (LQG) framework. Compared with other safety assessment methods, our framework allows the planner to avoid unsafe situations more efficiently, thanks to the direct uncertainty information feedback to the planner. We also demonstrate our planner’s ability to generate safer trajectories compared to planning only with a LQG framework.

Path planning using 3D Dubins Curve for Unmanned Aerial Vehicles

Abstract: We present a path planning algorithm based on 3D Dubins Curves [1] for Unmanned Aerial Vehicles (UAVs) to avoid both static and moving obstacles. A variation of Rapidly-exploring Random Tree (RRT) [2] is used as the planner. In tree expansion, branches of the tree are generated by propagating along 3D Dubins Curves. The node sequence of shortest length together with Dubins curves connecting them is selected as the path. When the UAV executes the path, the path is checked for collision with updated obstacles' states. A new path is generated if the previous one is predicted to collide with obstacles. Such checking and replanning loop repeats until the UAV reaches the goal. The algorithm was validated through flight experiments using a small quadrotor UAV. In total, 6 flights to avoid static obstacles, 24 flights to avoid virtual moving obstacles and 20 flights to avoid real moving obstacles were performed. The efficacy of the algorithm was tested in office conditions and a parking structure. In all the situations our algorithm was able to reliably plan paths in real time and command the UAV to avoid obstacles.

Asymptotically Optimal Sampling-based Kinodynamic Planning

Abstract: Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.

A natural language planner interface for mobile manipulators

Abstract: Natural language interfaces for robot control aspire to find the best sequence of actions that reflect the behavior intended by the instruction. This is difficult because of the diversity of language, variety of environments, and heterogeneity of tasks. Previous work has demonstrated that probabilistic graphical models constructed from the parse structure of natural language can be used to identify motions that most closely resemble verb phrases. Such approaches however quickly succumb to computational bottlenecks imposed by construction and search the space of possible actions. Planning constraints, which define goal regions and separate the admissible and inadmissible states in an environment model, provide an interesting alternative to represent the meaning of verb phrases. In this paper we present a new model called the Distributed Correspondence Graph (DCG) to infer the most likely set of planning constraints from natural language instructions. A trajectory planner then uses these planning constraints to find a sequence of actions that resemble the instruction. Separating the problem of identifying the action encoded by the language into individual steps of planning constraint inference and motion planning enables us to avoid computational costs associated with generation and evaluation of many trajectories. We present experimental results from comparative experiments that demonstrate improvements in efficiency in natural language understanding without loss of accuracy.