scholarly journals Task and Motion Planning Is PSPACE-Complete

2020 ◽  
Vol 34 (06) ◽  
pp. 10385-10392
Author(s):  
William Vega-Brown ◽  
Nicholas Roy
Keyword(s):  
Motion Planning ◽  
General Problem ◽  
Symbolic Representation ◽  
Technical Condition ◽  
Problem Instance ◽  
Planning Problem ◽  
Polynomial Space ◽  
Unified Framework ◽  
Robotic Planning

We present a new representation for task and motion planning that uses constraints to capture both continuous and discrete phenomena in a unified framework. We show that we can decide if a feasible plan exists for a given problem instance using only polynomial space if the constraints are semialgebraic and all actions have uniform stratified accessibility, a technical condition closely related to both controllability and to the existence of a symbolic representation of a planning domain. We show that there cannot exist an algorithm that solves the more general problem of deciding if a plan exists for an instance with arbitrary semialgebraic constraints. Finally, we show that our formalism is universal, in the sense that every deterministic robotic planning problem can be well-approximated within our formalism. Together, these results imply task and motion planning is PSPACE-complete.

scholarly journals Learning to guide task and motion planning using score-space representation

2019 ◽  
Vol 38 (7) ◽  
pp. 793-812 ◽  
Author(s):  
Beomjoon Kim ◽  
Zi Wang ◽  
Leslie Pack Kaelbling ◽  
Tomás Lozano-Pérez
Keyword(s):  
Motion Planning ◽  
Learning Algorithm ◽  
Search Space ◽  
Sequential Algorithm ◽  
Problem Instance ◽  
Space Representation ◽  
Planning Problem ◽  
Generic Representation ◽  
Planning Problems ◽  
Improve Planning

In this paper, we propose a learning algorithm that speeds up the search in task and motion planning problems. Our algorithm proposes solutions to three different challenges that arise in learning to improve planning efficiency: what to predict, how to represent a planning problem instance, and how to transfer knowledge from one problem instance to another. We propose a method that predicts constraints on the search space based on a generic representation of a planning problem instance, called score-space, where we represent a problem instance in terms of the performance of a set of solutions attempted so far. Using this representation, we transfer knowledge, in the form of constraints, from previous problems based on the similarity in score-space. We design a sequential algorithm that efficiently predicts these constraints, and evaluate it in three different challenging task and motion planning problems. Results indicate that our approach performs orders of magnitudes faster than an unguided planner.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

2003 ◽  
Author(s):  
Xin-Sheng Ge ◽  
Li-Qun Chen
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Nonholonomic System ◽  
Multibody System ◽  
Planning Problem ◽  
Control Approach ◽  
Velocity Constraints ◽  
Nonholonomic Motion Planning ◽  
Optimal Control Approach ◽  
Motion Planning Problem

The motion planning problem of a nonholonomic multibody system is investigated. Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the control problem of system can be converted to the motion planning problem for a driftless control system. In this paper, we propose an optimal control approach for nonholonomic motion planning. The genetic algorithm is used to optimize the performance of motion planning to connect the initial and final configurations and to generate a feasible trajectory for a nonholonomic system. The feasible trajectory and its control inputs are searched through a genetic algorithm. The effectiveness of the genetic algorithm is demonstrated by numerical simulation.

Motion planning problem with obstacle avoidance for step-2 bracket-generating systems

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 799-800 ◽  
Author(s):  
Victoria Grushkovskaya ◽  
Alexander Zuyev
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Planning Problem ◽  
Motion Planning Problem

scholarly journals Efficient Planning of Humanoid Motions by Modifying Constraints

2013 ◽  
Vol 4 (1) ◽  
Author(s):  
ChangHyun Sung ◽  
Takahiro Kagawa ◽  
Yoji Uno
Keyword(s):  
Motion Planning ◽  
Sufficient Conditions ◽  
Computation Time ◽  
Humanoid Robots ◽  
Body Motion ◽  
Whole Body ◽  
Planning Problem ◽  
Point Representation ◽  
Efficient Planning ◽  
Unpredictable Environment

AbstractIn this paper, we propose an effective planning method for whole-body motions of humanoid robots under various conditions for achieving the task. In motion planning, various constraints such as range of motion have to be considered. Specifically, it is important to maintain balance in whole-body motion. In order to be useful in an unpredictable environment, rapid planning is an essential problem. In this research, via-point representation is used for assigning sufficient conditions to deal with various constraints in the movement. The position, posture and velocity of the robot are constrained as a state of a via-point. In our algorithm, the feasible motions are planned by modifying via-points. Furthermore, we formulate the motion planning problem as a simple iterative method with a Linear Programming (LP) problem for efficiency of the motion planning. We have applied the method to generate the kicking motion of a HOAP-3 humanoid robot. We confirmed that the robot can successfully score a goal with various courses corresponding to changing conditions of the location of an obstacle. The computation time was less than two seconds. These results indicate that the proposed algorithm can achieve efficient motion planning.

Efficient Human Motion Planning Using Recursive Dynamics and Optimal Control Techniques

1999 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Closed Loop ◽  
High Efficiency ◽  
Human Motion ◽  
Lagrangian Formulation ◽  
Planning Problem ◽  
Tree Structures ◽  
Recursive Dynamics ◽  
Minimum Torque

Abstract We present an efficient optimal control based approach to simulate dynamically correct human movements. We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. To overcome the complexity limitations of the classical Lagrangian formulation and to include knowledge from biomechanical studies, we have developed a minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Our dynamic motion planning methodology achieves high efficiency regardless of the figure topology. As opposed to a Lagrangian formulation, it obviates the need for the reformulation of the dynamic equations for different structured articulated figures. We use a quasi-Newton method based nonlinear programming technique to solve our minimum torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. The results demonstrate that our approach generates natural looking and physically correct human motions.

scholarly journals A sampling-based optimized algorithm for task-constrained motion planning

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984737 ◽  
Author(s):  
Kai Mi ◽  
Haojian Zhang ◽  
Jun Zheng ◽  
Jianhua Hu ◽  
Dengxiang Zhuang ◽  
...  
Keyword(s):  
Motion Planning ◽  
Sampling Methods ◽  
Tracking Error ◽  
Joint Space ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Task Space ◽  
Constrained Motion ◽  
Smooth Path ◽  
Planning Algorithm

We consider a motion planning problem with task space constraints in a complex environment for redundant manipulators. For this problem, we propose a motion planning algorithm that combines kinematics control with rapidly exploring random sampling methods. Meanwhile, we introduce an optimization structure similar to dynamic programming into the algorithm. The proposed algorithm can generate an asymptotically optimized smooth path in joint space, which continuously satisfies task space constraints and avoids obstacles. We have confirmed that the proposed algorithm is probabilistically complete and asymptotically optimized. Finally, we conduct multiple experiments with path length and tracking error as optimization targets and the planning results reflect the optimization effect of the algorithm.

Solving the motion planning problem by using neural networks

Robotica ◽  
1994 ◽  
Vol 12 (4) ◽  
pp. 323-333 ◽  
Author(s):  
R.H.T. Chan ◽  
P.K.S. Tam ◽  
D.N.K. Leung
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Motion Planning ◽  
Configuration Space ◽  
Logic Gates ◽  
Moving Object ◽  
Planning Problem ◽  
Processing Unit ◽  
Configuration Point ◽  
Motion Planning Problem

SUMMARYThis paper presents a new neural networks-based method to solve the motion planning problem, i.e. to construct a collision-free path for a moving object among fixed obstacles. Our ‘navigator’ basically consists of two neural networks: The first one is a modified feed-forward neural network, which is used to determine the configuration space; the moving object is modelled as a configuration point in the configuration space. The second neural network is a modified bidirectional associative memory, which is used to find a path for the configuration point through the configuration space while avoiding the configuration obstacles. The basic processing unit of the neural networks may be constructed using logic gates, including AND gates, OR gates, NOT gate and flip flops. Examples of efficient solutions to difficult motion planning problems using our proposed techniques are presented.

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