Problem Of Trajectory Planning Research Articles

VSGA Method Based Trajectory Planning of a Novel Limb-robot

A new progressive genetic algorithm (PGA) was developed for trajectory planning of a novel limb-robot. The proposed trajectory planning method can be applied to get an optimal joints trajectory from the initial to the end position and orientation. On the basis of the genetic algorithm a new kind of variable structure genetic algorithm (VSGA) is proposed to solve the problem of trajectory planning of the limb-robot in complicate environments. The VSGA changes the original structure by abandoning Elitist Model, expectation selection, reproducing population and changing the probability of crossover and mutation. Experiments results show that the PGA is effective in static environments and the VSGA does well in complicate environments. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2564 Full Text: PDF

Trajectory Planning in Robotics

Trajectory planning is a fundamental issue for robotic applications and automation in general. The ability to generate trajectories with given features is a key point to ensure significant results in terms of quality and ease of performing the required motion, especially at the high operating speeds necessary in many applications. The general problem of trajectory planning in Robotics is addressed in the paper, with an overview of the most significant methods, that have been proposed in the robotic literature to generate collision-free paths. The problem of finding an optimal trajectory for a given path is then discussed and some significant solutions are described.

Splines and polynomial tools for flatness-based constrained motion planning

This article addresses the problem of trajectory planning for flat systems with constraints. Flat systems have the useful property that the input and the state can be completely characterised by the so-called flat output. We propose a spline parametrisation for the flat output, the performance output, the states and the inputs. Using this parametrisation the problem of constrained trajectory planning can be cast into a simple quadratic programming problem. An important result is that the B-spline parametrisation used gives exact results for constrained linear continuous-time system. The result is exact in the sense that the constrained signal can be made arbitrarily close to the boundary without having intersampling issues (as one would have in sampled-data systems). Simulation examples are presented, involving the generation of rest-to-rest trajectories. In addition, an experimental result of the method is also presented, where two methods to generate trajectories for a magnetic-levitation (maglev) system in the presence of constraints are compared and each method's performance is discussed. The first method uses the nonlinear model of the plant, which turns out to belong to the class of flat systems. The second method uses a linearised version of the plant model around an operating point. In every case, a continuous-time description is used. The experimental results on a real maglev system reported here show that, in most scenarios, the nonlinear and linearised models produce almost similar, indistinguishable trajectories.

GPU based generation of state transition models using simulations for unmanned surface vehicle trajectory planning

This paper describes GPU based algorithms to compute state transition models for unmanned surface vehicles (USVs) using 6 degree of freedom (DOF) dynamics simulations of vehicle–wave interaction. A state transition model is a key component of the Markov Decision Process (MDP), which is a natural framework to formulate the problem of trajectory planning under motion uncertainty. The USV trajectory planning problem is characterized by the presence of large and somewhat stochastic forces due to ocean waves, which can cause significant deviations in their motion. Feedback controllers are often employed to reject disturbances and get back on the desired trajectory. However, the motion uncertainty can be significant and must be considered in the trajectory planning to avoid collisions with the surrounding obstacles. In case of USV missions, state transition probabilities need to be generated on-board, to compute trajectory plans that can handle dynamically changing USV parameters and environment (e.g., changing boat inertia tensor due to fuel consumption, variations in damping due to changes in water density, variations in sea-state, etc.). The 6 DOF dynamics simulations reported in this paper are based on potential flow theory. We also present a model simplification algorithm based on temporal coherence and its GPU implementation to accelerate simulation computation performance. Using the techniques discussed in this paper we were able to compute state transition probabilities in less than 10 min. Computed transition probabilities are subsequently used in a stochastic dynamic programming based approach to solve the MDP to obtain trajectory plan. Using this approach, we are able to generate dynamically feasible trajectories for USVs that exhibit safe behaviors in high sea-states in the vicinity of static obstacles.

Energy-optimal trajectory planning for the Pendubot and the Acrobot

SUMMARY In this paper, we study the trajectory-planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler–Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity. Copyright © 2012 John Wiley & Sons, Ltd.

Differentially Flat Designs of Underactuated Mobile Manipulators

This paper presents a methodology for design of mobile vehicles, mounted with underactuated manipulators operating in a horizontal plane, such that the combined system is differentially flat. A challenging question of how to perform point-to-point motions in the state space of such a highly nonlinear system, in spite of the absence of some actuators in the arm, is answered in this paper. We show that, by appropriate inertia distribution of the links and addition of torsion springs at the joints, a range of underactuated designs is possible, where the underactuated mobile manipulator system is differentially flat. The differential flatness property allows one to efficiently solve the problem of trajectory planning and feedback controller design for point-to-point motions in the state space. The proposed method is illustrated by the example of a mobile vehicle with an underactuated three-link manipulator.

Stochastic Multi-objective Optimization for Aggressive Maneuver Trajectory Planning on Loose Surface

In this work we regard the problem of trajectory planning for aggressive maneuver of a wheeled mobile robot on loose surface. Our approach is inspired by previously reported analysis of professional rally racers actions during sharp turn. Using numerical simulations we obtain a set of solutions representing all possible compromises between speed and accuracy of maneuver. We choose a particular solution and extend it by producing a continuous mapping from desired trajectory turn angles to parameters of the control inputs.

2P1-E26 移動障害物を回避するための軌道生成アルゴリズム

Nowadays, we can see the use of mobile robots in various environments close to human life such as offices, hospitals. So it is important to solve the problem of trajectory planning under the environment which has moving objects like human beings. This paper poroposes an algorithm of trajectory plannning conbined potential method and particle control for a mobile robot to avoid moving objects. With this algorithm, a mobile robot can move safely under the continuous dynamic environment that has moving objects.

Race driver model

The best race driver is the one that, with a given vehicle, is able to drive on a given track in the shortest possible time. Thus, the only target is the lap time. A race driver model has to do the same. The first step towards this target is to decide which trajectory to follow. In fact, the optimal trajectory is the best compromise between the shortest track and the track that allows to achieve the highest speeds (least curvature track). Thus, the problem of trajectory planning is a bounded optimisation problem that has to take into account not only the geometry of the circuit but also the dynamics of the vehicle. A simplified vehicle dynamic model is used for this purpose. Due to the fact that the vehicle will be driven at its limit performances, although simplified, the model has to correctly reproduce the maximum possible acceleration, a function of the vehicle speed, the maximum possible deceleration, again a function of the vehicle speed, and the maximum lateral acceleration, a function of both the vehicle speed and the steering angle. Knowing the trajectory, the vehicle model allows to determine the lap time. Through an optimisation algorithm it is therefore possible to determine the best compromise between shortest track and track with the minimum curvature, i.e. the trajectory (in terms of track and speed profile) that allows to minimize the time lap. Once the best trajectory has been determined (both in terms of best track and best speed profile), it is necessary to identify the driver’s inputs to follow the given trajectory. This task is carried out by considering the driver as a controller that acts on a nonlinear plant (the vehicle) in order to achieve the desired results. Thus, the driver converts the best trajectory into vehicle’s inputs. The mutual interaction between plant and controller (the driver’s inputs are not only a function of the best trajectory but also of the driver’s reactions due to the vehicle’s dynamics) is not taken into account in this paper.

Planar trajectory planning and tracking control design for underactuated AUVs

This paper addresses the combined problem of trajectory planning and tracking control for underactuated autonomous underwater vehicles (AUVs) on the horizontal plane. Given a smooth, inertial, 2D reference trajectory, the planning algorithm uses vehicle dynamics to compute the reference orientation and body-fixed velocities. Using these, the error dynamics are obtained. These are stabilized using backstepping techniques, forcing the tracking error to an arbitrarily small neighborhood of zero. Simulation results for a constant velocity trajectory, i.e. a circle, and a time-varying velocity one, i.e. a sinusoidal path, are presented. The parametric robustness is considered and it is shown that tracking remains satisfactory.

Fuzzy-GA-based trajectory planner for robot manipulators sharing a common workspace

This paper presents a novel fuzzy genetic algorithm (GA) approach to tackling the problem of trajectory planning of two collaborative robot manipulators sharing a common workspace, where the manipulators have to consider each other as a moving obstacle whose trajectory or behaviour is unknown and unpredictable, as each manipulator has individual goals and where both have the same priority. The goals are not restricted to a given set of joint values, but are specified in the workspace as coordinates at which it is desired to place the end-effector of the manipulator. By not constraining the goal to the joint space, the number of possible solutions that satisfies the goal increases according to the number of degrees of freedom of the manipulators. A simple GA planner is used to produce an initial estimation of the movements of the robots' articulations and collision free motion is obtained by the corrective action of the collision-avoidance fuzzy units

Planning under uncertainty using model predictive control for information gathering

This paper considers trajectory planning problems for autonomous robots in information gathering tasks. The objective of the planning is to maximize the information gathered within a finite time horizon. It is assumed that either the Extended Kalman Filter (EKF) or the Extended Information Filter (EIF) is applied to estimate the features of interest and the information gathered is expressed by the covariance matrix or information matrix. It is shown that the planning process can be formulated as an optimal control problem for a nonlinear control system with a gradually identified model. This naturally leads to the Model Predictive Control (MPC) planning strategy, which uses the updated knowledge about the model to solve a finite horizon optimal control problem at each time step and only executes the first control action. The proposed MPC framework is demonstrated through solutions to two challenging information gathering tasks: (1) Simultaneous planning, localization, and map building (SPLAM) and (2) Multi-robot Geolocation. It is shown that MPC can effectively deal with dynamic constraints, multiple robots/features and a range of objective functions.

A multi-link system control strategy based on biological reaching movement

In the multi-link arm control process, the problems of trajectory planning and trajectory realization have been recognized as being of key importance. We developed a technique by which to realize a reaching movement control of the multi-link arm system, which was inspired by experimental results for reaching movements of macaques or human beings. The proposed method can treat the effect of the dynamics of the multi-link system and the trajectory planning of the end-effector, which has a bell-shaped speed profile, as well as the difficulties of redundancies of multi-link systems. Two-link arm reaching movement experiments revealed the same features, as demonstrated by the results of biological experiments on humans and macaques. In addition, the results obtained using a two-dimensional four-link model in a standing-up movement control experiment agreed well with 'standing-up from a chair' movement of human beings. Since the proposed method has a simple structure and its implementation process is simple, the proposed method will be effective for use in a multi-link system control strategy.

Coordination Variables, Coordination Functions, and Cooperative Timing Missions

A solution strategy for achieving cooperative timing among teams of vehicles is presented. Based on the notion of coordination variables and coordination functions, the strategy facilitates cooperative timing by making efficient use of communication and computation resources. The application of the coordination variable/function approach to trajectory-planning problems for teams of unmanned air vehicles with timing constraints is described. Three types of timing constraints are considered: simultaneous arrival, tight sequencing, and loose sequencing. Simulation results demonstrating the viability of the approach are presented.

Dynamic Feedback Control of XYnR̄ Planar Robots with n Rotational Passive Joints

AbstractWe consider the problem of trajectory planning and control for an XYnR̄ Planar robot with the first two joints (rotational or prismatic) actuated and n rotational passive joints, moving both in the presence and the absence of gravity. Under the assumption that each passive link is attached at the center of percussion of the previous passive link, dynamics of the system can be expressed through the behavior of n special points of the plane. These points are called link‐related acceleration points (LRAP) since their instantaneous acceleration is oriented as the axis of the related passive links. Moreover, LRAP dynamics present a backward recursive form which can be exploited to recursively design a dynamic feedback that completely linearizes the system equations. We use this approach to solve trajectory planning and tracking problems and report simulation results obtained for an RR2R̄ robot having the first two rotational joints actuated. © 2003 Wiley Periodicals, Inc.

Trajectory Planning of Mobile Manipulator with Stability Considerations

In this paper, a problem of trajectory planning for a mobile manipulator with stability considerations is presented. We derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. As a measure for the system stability, a ZMP criterion is used. The planning problem is formulated as an optimal control problem with some constraints. To solve the problem, we use a hierarchical gradient method which synthesizes the gradient function in a hierarchical manner based on the order of priority. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

Preview-Based Stable-Inversion for Output Tracking of Linear Systems

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is noncausal—hence the inverse has to be precomputed using a prespecified desired-output trajectory. This requirement for prespecification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output-tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Trajectory planning of multiple coordinating robots using genetic algorithms

SUMMARYThe paper focuses on the problem of trajectory planning of multiple coordinating robots. When multiple robots collaborate to manipulate one object, a redundant system is formed. There are a number of trajectories that the system can follow. These can be described in Cartesian coordinate space by an nth order polynomial. This paper presents an optimisation method based on the Genetic Algorithms (GAs) which chooses the parameters of the polynomial, such that the execution time and the drive torques for the robot joints are minimized. With the robot's dynamic constraints taken into account, the pitimised trajectories are realisable. A case study with two planar-moving robots, each having three degrees of freedom, shows that the method is effective.

Performance of Several Optimization Methods on Robot Trajectory Planning Problems

Previous article Next article Performance of Several Optimization Methods on Robot Trajectory Planning ProblemsJoseph G. Ecker, Michael Kupferschmid, and Samuel P. MarinJoseph G. Ecker, Michael Kupferschmid, and Samuel P. Marinhttps://doi.org/10.1137/0915084PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper provides a comparison and analysis of the performance of a special purpose algorithm and several specific available nonlinear programming codes applied to a robot trajectory problem.[1] Mokhtar S. Bazaraa and , C. M. Shetty, Nonlinear programming, John Wiley & Sons, New York-Chichester-Brisbane, 1979xiv+560 80f:90110 0476.90035 Google Scholar[2] C. deBoor, A practical guide to splines, Applied Mathematical Sciences, Vol. 27, Springer-Verlag, New York, 1978xxiv+392 80a:65027 0406.41003 CrossrefGoogle Scholar[3] A. Ech-Cherif, , J. G. Ecker, , M. Kupferschmid and , S. P. Marin, Robot Trajectory Planning by Nonlinear Programming, General Motors Research Publication, GMR-6460, General Motors Research Laboratories, Warren, MI, 1988, December Google Scholar[4] J. G. Ecker and , M. Kupferschmid, A computational comparison of the ellipsoid algorithm with several nonlinear programming algorithms, SIAM J. Control Optim., 23 (1985), 657–674 10.1137/0323042 86j:90127 0581.90078 LinkISIGoogle Scholar[5] J. G. Ecker and , M. Kupferschmid, Introduction to Operations Research, Wiley, New York, 1988 0647.90053 Google Scholar[6] D. Goldfarb and , A. Idnani, A numerically stable dual method for solving strictly convex quadratic programs, Math. Programming, 27 (1983), 1–33 84k:90058 0537.90081 CrossrefISIGoogle Scholar[7] Users Manual Math/Library, Sugarland, TX, 1987, April Google Scholar[8] M. Kupferschmid and , J. G. Ecker, EA3: A Practical Implementation of an Ellipsoid Algorithm for Nonlinear Programming, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 1984 Google Scholar[9] L. S. Lasdon, , A. Waren, , A. Jain and , M. W. Ratner, Design and testing of a generalized reduced gradient code for nonlinear programming, Trans. Math. Software, 4 (1978), 34–50 10.1145/355769.355773 0378.90080 CrossrefGoogle Scholar[10] S. P. Marin, Optimal Parametrization of Curves in RN, General Motors Research Publication, GMR-4878, General Motors Research Laboratories, Warren, MI, 1985, August Google Scholar[11] S. P. Marin, Optimal parametrization of curves for robot trajectory design, IEEE Trans. Automat. Control, 33 (1988), 14–31 10.1109/9.393 CrossrefISIGoogle Scholar[12] M. J. D. Powell, VMCWD: A Fortran Subroutine for Constrained Optimization, Paper DAMTP, 1982/NA4, Dept. of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1982 Google Scholar[13] K. Schittkowski, NLPQL: a FORTRAN subroutine solving constrained nonlinear programming problems, Ann. Oper. Res., 5 (1986), 485–500 89d:90200 CrossrefGoogle ScholarKeywordsnonlinear programmingalgorithm evaluationrobot modeling Previous article Next article FiguresRelatedReferencesCited ByDetails On the Minimum-Time Control Problem for Differential Drive Robots with Bearing ConstraintsJournal of Optimization Theory and Applications, Vol. 173, No. 3 | 11 April 2017 Cross Ref Calculating a near time-optimal jerk-constrained trajectory along a specified smooth pathThe International Journal of Advanced Manufacturing Technology, Vol. 45, No. 9-10 | 19 April 2009 Cross Ref Volume 15, Issue 6| 1994SIAM Journal on Scientific Computing1251-1505 History Submitted:05 December 1988Accepted:21 September 1993Published online:13 July 2006 InformationCopyright © 1994 Society for Industrial and Applied MathematicsKeywordsnonlinear programmingalgorithm evaluationrobot modelingMSC codes90PDF Download Article & Publication DataArticle DOI:10.1137/0915084Article page range:pp. 1401-1412ISSN (print):1064-8275ISSN (online):1095-7197Publisher:Society for Industrial and Applied Mathematics

The synthesis of smooth Cartesian trajectories for pick-and-place operations of spherical wrists

The off-line synthesis of Cartesian trajectories of spherical wrists capable of orienting their end effector arbitrarily in space is the subject of this paper. Thus, serial and parallel, non-redundant and redundant wrists are considered, for the method reported here is architecture independent. Motions undergone by spherical wrists are regarded as points on the surface of the unit sphere centered at the origin of the 4-D space of the variables used to describe the motion. Furthermore, the projection of this sphere onto the 3-D space of the invariant vector of the rotation under study, a solid unit sphere centered at the origin of that 3-D space, yields a straightforward geometric interpretation of this motion. Thus, a rigid-body rotation given as a smooth function of time appears as a smooth curve within the unit sphere of this 3-D space. Moreover, an explicit relation between the time derivative of the said Cartesian vector and the angular-velocity vector yields the kinematic interpretation of the velocity of the point tracing that curve. This concept is applied to the problem of trajectory planning for robotics pick-and-place operations, resorting to a normal trajectory.