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1、Path Control in Robotics,ME 4135 Lecture series 8 Richard R. Lindeke, Ph. D.,Motion Types of Interest,Point to Point Motion: All Axes start and end simultaneously All Geometry is computed for targets and relevant Joint changes which are then forced to be followed during program execution Path or Tra
2、jectory Controller Motion Here the motion is performed through a time sequence of intermediate configurations computed ahead of time (like above but without stop-start operation) or in real time Paths are “Space Curves” for the n-Frame to follow This motion is a continuous scheme to move the TCP fro
3、m one location to the next along a desired (straight or curved) line under direct operational control,Path Control and Motion Types:,We will explore the following types of Motion: Lead Through Path Creation (Cubic) Polynomial Paths w/ Via Points Minimum Time Trajectory w/ controlled Acceleration Low
4、er order Path-Poly Control LSPB Paths Craigs Method for acceleration smoothing Strict Velocity Control Joint Interpolated Control Full Cartesian Control,Basically this was a technique whereby a skilled operator took a robot arm (for welding or painting) and used it like his/her weld tool or paint sp
5、rayer and performed the required process at reasonable speed The robot is equipped with a position recording device and memorizes a large number of points during the teaching session These learned points then would be “played back” to replicate the skilled operators motions,Lead Through Path Creatio
6、n,Lead Through Path Creation,Advantages: Simple way to create complex paths All points are sure to be physically attainable Playback speed can be controlled by an external device Disadvantages: Precision placements are required (program must be replayed at exactly the initial placement) Major concer
7、n with operator safety: robot is powered and operator is physically touching it (OSHA rules it unsafe practice!),Modern Path Control: (Lets look at a simple example),Dr. Ds new Self-powered Automated Coffee Drinker Robot It is a simple cantilevered Cartesian device equipped with a spherical wrist th
8、at responds to eye movement and thoughts to help the overworked design engineer get coffee while designing and drafting & typing of Reports It follows a straight line path from the cups point on a table to the workers mouth in second,Lets look at a simple example:,Lets look at a simple example:,We s
9、ee that the Bot must travel a space path of 16.45” which can be decomposed into a movement of 9.5” along each of the prismatic joints For accuracy lets divide each of the these joint paths into 100 segments From Physics: Vjoint d/ t = (9.5/100)/(.5/100) = 19in/second (a reasonable speed!),Lets look
10、at a simple example:,During the 1st Step then: Joint 1 starts at 0 and moves to 0.095” Moves there in 0.005 seconds How will it do it? Of course by Accelerating from a stop to 19 in/sec in 0.005 seconds Compute Accreqr V/t,Darn this says that the acceleration is 3800in/sec2 this is 10G!,Lets look at
11、 a simple example:,So this will certainly be difficult to accomplish! (more likely it will not work) OSHA would be just as upset as when we had the worker holding on to the powered robot what should we do? I think our approach is too nave! If we examine the Pos vs. Time, Vel Vs. Time and Acc vs. Tim
12、e plots we may see why:,Look at a simple examples Trajectory Curves:,This is Physically Impossible (or rather very energy intensive),Can we build a reasonable solution that keeps the acceleration to an achievable level? What this would mean is we wouldnt “instantly” in one time step go from stopped
13、to full speed This can be achieved with a “time polynomial” model of motion,Building a Path Polynomial Motion Set,These are the trajectory equations for a joint (Position, Velocity and Acceleration),Solving the Path Polynomial is a matter of finding ais for SPECIFIC PATHS,We would have “boundary” co
14、nditions for position and velocity at both ends of the path We would have the desired total time of travel Using these conditions we can solve for a0, a1, a2 and a3 to build a 3rd order path polynomial for the required motion,Solving the Path Polynomial is a matter of finding ais for specific paths,
15、Polys holding at starting time and position,Polys holding at ending time and position,Solving the Path Polynomial is a matter of finding ais for specific paths,Writing these as Matrix Forms:,Solving the Path Polynomial is a matter of finding ais for specific paths,If we set t0 = 0 (starting time is
16、when we start counting motion!) then:,By examination, a0 = q0 & a1 = q0(dot),Solving the Path Polynomial is a matter of finding ais for specific paths,Completing the solution consists of forming relationships for: a2 & a3 Done by substituting a0 & a1 values and solving the last two equation simultaneously:,Be Careful and note the order of the positions and velocities!,Applying it to the Coffee Bot,Start: X = 0; v = 0 time = 0 End: X = 9.5”; v = 0 time = .5 sec a0 = 0 ; a1 = 0 a2 = (3 * 9.5)/(0.52) = 114 a3 = (2 *(- 9.5)/(0.53) = -152,
