Trajectory Beed and Movement of the 4-DOF Handling Manipulator - Term Paper Example

Trajectory planning A trajectory is the pathway tagged along by the manipulator, together with the time profile alongside the path. Trajectories can be prepared either in Cartesian space (stipulating the position and compass reading to the end frame) or in joint space (exactly stipulating the evolution time of the joint angles). It is necessary to consider the following aspect during the trajectory planning; avoid obstacles, reach a given target from a preliminary starting point and stay within manipulator capabilities. Planning in joint space is so simple and quick, since inverse kinematics is circumvented. The downside is that the end affecter pose is not controlled directly, thus it becomes difficult to avoid collision. On other hand, to plan in Cartesian space more directly permits the geometric constraints of the exterior globe to be met, however, the inverse kinematics have to be solved. Many people normally wonder how trajectories are represented in computers after they have been planned. Representation takes place at run time; frequently, velocity, position, and acceleration are computed on digital computers. Therefore, trajectory points are computed at a particular rate that is known as path-update rate. In archetypal manipulator systems, this rate rages from 60 to 2000 Hz. General consideration in path description and generation A motion of a manipulator is taken as motions of the tool frame (t), relative to the frame station, (s). This is a similar way in which an ultimate user of the system may imagine, and designing a description path, but the consequences of this generation system will be disadvantageous. When a path is described as a motion of the tool frame equal to the station frame, the motion description is decoupled from any given robot or work-pieces. Basic problems encountered in moving a robot from the start position given by the tool frame Tinitial to the end position by the tool frame Tfinal include: Spatial Motion constraints like; specification of motion might be include so called via points, and Via points there might be intermediate points between start and end points. Temporal motion Constraints; whereby motion specification might include elapsed time between points. For a good trajectory, there should be execution of smooth motions; it should function smoothly where its function and firs derivative is continuous, and jerky motions increases wear on the mechanism (gears) and cause vibrations by exciting resonance of the robot. Trajectory in joint space In PTP motions the path shape in space and time are described in terms of functions of joint angles. The path joints are described via points including the start and end point in terms of tool frames. Each path joint is converted into joint angles by the application of inverse kinematics. Identifying a smooth function for each of the n joints passing through via points and ends at the target point. The above figure shows PTP motion between two points Advantages of PTP motions In between via points, the shape of the path is complex is described in Cartesian space Joint space trajectory generation schemes are easy to compute. Each joint motion is calculated independently from other joints. Many, actually infinite, smooth functions exist for such motions Four constraints on the (single) joint function q(t) are evident: Start configuration q(0) = qA , end configuration end B q(tend ) = q Velocities q(0) = 0, q(tend ) = 0 Four constraints can be satisfied by a polynomial of degree 3 or higher. In case of via points the velocity is not zero. Start configuration q(0) = qA , end configuration end B q(tend ) = q Velocities q(0) = q0, q(tend ) = qend Choosing velocities might either be either through the robot user or automatically chosen by the robot control. Using these types of polynomials does not in general generate time optimal motion. Linear function with parabolic blends Path with trapezoidal velocity profile Smooth motion constructed by adding parabolic blends to the linear function: In this process three assumptions are made: That there is constant acceleration during the blend; That the duration of the two parabolic blends is the same Therefore the symmetry is about the halfway point in time th In this case the velocity at the end of the blend ia equal to velocity during the linear section i.e. And qb=q0+1/2qt2b leads to qt2b – qttb + (qf - q0) = 0 Free parameters q and tb acceleration is usually chosen and the equation is solved for tb. For this case, the acceleration chosen must be sufficiently high to come up with a solution otherwise the solution will not exist; the acceleration should not be continuous in order to excite vibrations. Alternative: sinoidad profile Acceleration if defined by: q(t) = qmax .sin2 ( . t ) Profile for a sinusoidal path The following relationships are valid according to the sinusoidal profile Qmax = Tb = tv = tf - tb The constraint on the acceleration is t2 f.qmax >8.qf Calculation of q(t): 0 Read More