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3 axis robot trajectory without collision
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The paper presents a strategy for robotic exploration problems using Space-Filling curves (SFC). The region of interest is first tessellated, and the tiles/cells are connected using some SFC. A robot follows the SFC to explore the entire area. However, there could be obstacles that block the systematic movement of the robot. We overcome this proble...
Citations
... Papers [1][2][3][4] suggest generating algorithms of a reference trajectory, which are based on an arbitrary discretization of the manipulators internal coordinates. Each point of discretization in the external space approximating a reference trajectory corresponds with known discretized internal coordinates of the manipulator. ...
... In algorithms [1][2][3][4], based on an arbitrary discretization of the manipulator's internal coordinates, a discretized description of the manipulator external space results from the discretized description of its internal space. A reference trajectory in the external space is approximated using just such a discretized description of the manipulator external space. ...
... What follows from the foregoing review is that the kinematics models as presented in [1][2][3][4][5][6][7]16] do not allow one to design accurate, and at the same time fast, reference trajectory generating algorithms with a defined kinematics for under 6 degrees of freedom manipulators. ...
The fundamental problem in industrial robots control concerns algorithms generating reference trajectories.Papers [1–4] suggest generating algorithms of a reference trajectory, which are based on an arbitrary discretization of the manipulators internal coordinates. Each point of discretization in the external space approximating a reference trajectory corresponds with known discretized internal coordinates of the manipulator.In papers [5–7], iteration methods of determining the internal coordinates corresponding to external coordinates of the reference trajectory point have been suggested. In this method of internal coordinates, determining the point of the reference trajectory is being approached in successive steps of iterative computation. In paper [5], a modified iterative method of generating a reference trajectory straight segment has been presented.Analytic formulas which are the solution of an inverse problem of manipulator kinematics enable designing of trajectory generating algorithms which compute, in one step only, internal coordinates of points lying exactly on the reference trajectory, with the accuracy resulting from the computer register length.This paper presents equations of links and actuators kinematics of the IRb-6 manipulator in matrix form. Also, solutions of equations of link kinematics, as well as formulas joining link and actuator natural coordinates of the manipulator, have been presented.
... Additional internal jUcmms result from the division of actuator natural coordinates (within ranges corresponding to consecutive AFPs), and will be denoted using the abbreviation AIFP. Figure 3 shows the way in which the AIFPs between the (j -l)th and j th AFP are computed. Each range of actuator natural coordinates corresponding to consecutive AFPs is divided into N + 1 parts, where N is described by formula (2). It is assumed in the formula that the minimal angular ratio for orientation errors is equal to I/Q (1 -Ics)l (/cd = -128, Its = 19/32, see [8,18]): ...
The fundamental problem in industrial robots control concerns algorithms generating reference trajectories.References [1–4] suggest generating algorithms of a reference trajectory, which are based on an arbitrary discretization of the manipulator's internal coordinates. Each point of discretization in the external space approximating a reference trajectory corresponds to known discretized internal coordinates of the manipulator.In [5–7], iteration methods of determining the internal coordinates corresponding to external coordinates of the reference trajectory point have been suggested. In this method of internal coordinates, determining the point of the reference trajectory is being approached in successive steps of an iterative computation. In [5], a modified iterative method of generation of a straight segment reference trajectory has been presented.Analytic formulae, which are the solution of an inverse problem of manipulator kinematics, enable design of trajectory generating algorithms which compute, in one step only, the internal coordinates of points lying exactly on the reference trajectory, with the accuracy resulting from the computer register length.In this paper, the author has presented an original PLAN2 computer algorithm generating reference trajectories of motion for a task. The kinematics of those trajectories is defined at selected points through which a task is to be passed, the distances between them being optional. The algorithm is based on formulae which are analytic solutions to an inverse problem for an IRb-6 manipulator kinematics.
This chapter describes the development of an open-structure wheel-based mobile robotic platform and a complementary software simulator aimed at research, development and education, as well as the objective benchmarking of this kind of advanced mechatronic system. The main objectives of the work are concerned with solving the problems of development of an autonomous navigation system, motion planning and control of mobile robots in unstructured environments in the presence of mobile and immobile obstacles and system uncertainties such as a variation in tire-ground interaction.
A motion planner has been developed and implemented which can plan collision-free motions for serial manipulator arms with many degrees of freedom among stationary obstacles. The planner is based on a sequential search strategy that exploits the serial nature of manipulator arms. The motion of each link is planned successively starting from the base link. Given that the motion of links until link i has been planned, the motion of link i+1 is now planned along this collision-free path by controlling the degree of freedom associated with it. In the simplest case, this strategy results in one one-dimensional (the first link is degenerate) and n-1 two-dimensional planning problems instead of one n-dimensional problem for an n-link manipulator arm. The search strategy leads to a fast and efficient algorithm, and is especially suited for manipulator arms with many degrees of freedom. Furthermore, a backtracking mechanism has been incorporated in the planner which makes it more effective, but slower, in cluttered environments. This mechanism provides a parameter which can be used to trade off completeness of the planner with its speed. The effectiveness of the planner strategy is demonstrated with examples of motion planning for several arms with many degrees of freedom.
This chapter describes motion planning and obstacle avoidance for mobile robots. We will see how both areas do not share the
same modeling background. From the very beginning of motion planning, the research has been dominated by computer science.
Researchers aim at devising well-grounded algorithms with well-understood completeness and exactness properties. The introduction
of nonholonomic constraints has forced these algorithms to be revisited via the introduction of differential geometry approaches.
Such acombination has been made possible for certain classes of systems, so-called small-time controllable ones. The underlying
hypothesis of motion planning algorithms remains the knowledge of aglobal and accurate map of the environment. More than
that, the considered system is aformal system of equations that does not account for the entire physical system: uncertainties
in the world or system modeling are not considered. Such hypotheses are too strong in practice. This is why other complementary
researchers have adopted a parallel, more pragmatic but realistic approach to deal with obstacle avoidance. The problem here
is not to deal with complicated systems like acar with multiple trailers. The considered systems are much simpler with respect
to their geometric shape. The problem considers sensor-based motion to face the physical issues of areal system navigating
in areal world better than motion planning algorithms: how to navigate toward agoal in acluttered environment when the obstacles to avoid are discovered in real time? This is the question obstacle
avoidance addresses.
Performing complex assembly tasks requires decisional capabilities available on-line, in order to handle various events (sensor conditions, part arrivals, failure detection...), that occur during execution. In this paper, we describe NNS, a complete on-line system for multi-robot assembly workcells, that deals with problems of execution monitoring, action scheduling, and failure diagnosis and recovery. NNS is distributed in different decisional layers with their own reasoning methods and state representation; it uses an "execution model" that embeds various knowledge bases built off-line. This approach fits well with requirements of flexibility and efficiency.
The authors have implemented a motion planner based on a novel
sequential strategy to plan collision-free motions for serial
manipulator arms among 3D polyhedral obstacles. The basic idea is to
successively plan the motion of each link starting from the base link.
Suppose that the motion of links till link i (including link
i ) has been planned. This already determines the path of one
end (the proximal end) of link i +1. The motion of link i
+1 is now planned along this path by controlling the degree of
freedom associated with it-a 2D motion planning problem. This strategy
results in one 1D (for the first link) and n -1 2D planning
problems instead of one n -D problem. This greatly reduces
complexity and is especially suitable for highly redundant arms.
However, it is incomplete. Experimental results are given
The kinematic and dynamic modelling of robot manipulators are of such computational complexity that control schemes embodying on-line calculation of the robot model have previously been impossible at an economic cost in terms of computer hardware. However, the recent development of the transputer has transformed this situation, as shown in the paper. On-line schemes using transputers are shown to be feasible as solutions for two significant computational problems in manipulator control: computing the dynamic model, and computing a time-optimal path.
