1 00:00:00,270 --> 00:00:04,350 From this listen, we are starting the trajectory planning of robot manipulators. 2 00:00:04,560 --> 00:00:10,470 This is really interesting and exciting topic because it not only contains some math, but also it will 3 00:00:10,470 --> 00:00:13,740 help us to do interesting things with robot manipulators. 4 00:00:14,280 --> 00:00:18,690 So here are the topics that we have seen until today about robot manipulators. 5 00:00:19,140 --> 00:00:24,840 We have seen kinematics of robot manipulators where we discussed forward and inverse kinematics of robot 6 00:00:24,840 --> 00:00:25,620 manipulators. 7 00:00:26,130 --> 00:00:31,530 Then we have seen dynamics of robot manipulators where we got orderly, the information about how forces 8 00:00:31,530 --> 00:00:35,160 affect the position and orientation of robots manipulator. 9 00:00:35,790 --> 00:00:39,150 Now we are considering trajectory planning of robot manipulators. 10 00:00:39,720 --> 00:00:42,900 After that, we will see the control of robot manipulators. 11 00:00:43,320 --> 00:00:49,800 The reason we will study trajectory planning first is that we want to first create trajectory that robots 12 00:00:49,800 --> 00:00:54,270 will follow and then make robot follow it through some control algorithms. 13 00:00:55,430 --> 00:01:00,840 Let's let's assume that we have given the task of picking a place where we take an object from starting 14 00:01:00,840 --> 00:01:04,050 point and place it into the specified destination point. 15 00:01:04,350 --> 00:01:07,620 So what are the steps that we have to follow to do the task? 16 00:01:08,160 --> 00:01:13,410 We have to start the task planning where we try to specify the starting and destination point. 17 00:01:14,160 --> 00:01:20,190 Then we are doing path planning where we identify the intermediate points that enable us to go to the 18 00:01:20,190 --> 00:01:24,300 desired position without collision with obstacles and internal collisions. 19 00:01:24,720 --> 00:01:25,680 So is that all? 20 00:01:26,190 --> 00:01:31,800 Can we now control our robot and make it follow the calculated points and reach the destination? 21 00:01:32,280 --> 00:01:39,150 Yes, indeed we can do, but we shouldn't do that because every robot has its own specification and 22 00:01:39,150 --> 00:01:40,050 capabilities. 23 00:01:40,290 --> 00:01:45,000 It depends on its multiple ability, actuator specifications and so on. 24 00:01:45,420 --> 00:01:50,670 So we have to consider trajectory planning step also where we take time into consideration. 25 00:01:50,670 --> 00:01:56,790 Also, namely, we have to determine the velocities and accelerations of robot manipulator at each point 26 00:01:57,480 --> 00:01:58,070 we have. 27 00:01:59,490 --> 00:02:05,880 We have to make robot follow the given paths not in the arbitrary way, but in a smooth fashion, because 28 00:02:05,880 --> 00:02:11,010 robot manipulators actuators have velocity limits and torque limits, and we have to respect that. 29 00:02:11,910 --> 00:02:17,310 So from that discussion discussion, you can somehow understand the difference between the path and 30 00:02:17,310 --> 00:02:18,150 the trajectory. 31 00:02:18,600 --> 00:02:24,630 Path is pure geometric description of motion where we just specify the points that and the factor has 32 00:02:24,630 --> 00:02:25,200 to follow. 33 00:02:25,530 --> 00:02:31,140 These points can be determined either in joint space or in operational space, and we don't take into 34 00:02:31,140 --> 00:02:34,650 account time motion, namely velocity and acceleration. 35 00:02:35,040 --> 00:02:40,650 However, in terms of trajectory, we have to take into consideration timing low in terms of velocities 36 00:02:40,650 --> 00:02:45,060 and accelerations in order to provide smooth motion of robot manipulator. 37 00:02:45,330 --> 00:02:47,010 Without such rotating actuators. 38 00:02:47,670 --> 00:02:50,910 So let's summarize here why we need trajectory planning. 39 00:02:51,180 --> 00:02:56,610 First of all, we want to avoid abrupt motions of robot manipulator because it is not only dangerous 40 00:02:56,610 --> 00:03:01,470 for other objects near the robots, but also for the actuators of the robot joints. 41 00:03:01,950 --> 00:03:07,770 We want to take into account the actuator velocity and torque limits in order not to pass these limits 42 00:03:07,770 --> 00:03:11,220 and saturate actuators during reaching some destination point. 43 00:03:11,760 --> 00:03:14,240 And last but not least, we want to go. 44 00:03:14,460 --> 00:03:17,640 We want the coordination and synchronization of multiple bodies. 45 00:03:17,910 --> 00:03:23,550 Namely, for example, the robot manipulator consist of six joints or seven beings in order to reach 46 00:03:23,550 --> 00:03:24,610 the given point. 47 00:03:24,630 --> 00:03:28,080 Some joints have to move shorter, while others longer. 48 00:03:28,530 --> 00:03:35,790 We have to take this issue into consideration because we don't want some joints reach the desired configuration 49 00:03:35,790 --> 00:03:39,960 faster than others and stop while other joints still moving. 50 00:03:40,410 --> 00:03:45,360 We want them all to reach the final configuration at the same time and in a smooth way. 51 00:03:45,690 --> 00:03:49,770 Here we are confronted with the issue of coordination and synchronization. 52 00:03:50,640 --> 00:03:56,880 Finally, we can plan the trajectory for our robot manipulator in two ways, namely in joint space and 53 00:03:56,880 --> 00:03:58,860 in operational or task space. 54 00:03:59,190 --> 00:04:05,830 Both of these methods have their own advantages and disadvantages, namely when we plan the trajectory. 55 00:04:05,850 --> 00:04:12,360 One of the key issues is obtaining collision free trajectory as obstacles are in task space. 56 00:04:12,600 --> 00:04:19,470 We can consider obstacles in tasks based more easily so we can plan our trajectory in operational space 57 00:04:19,470 --> 00:04:20,370 or task space. 58 00:04:20,880 --> 00:04:26,490 However, after planning the trajectory, we have to execute it, but we cannot give the Cartesian coordinates 59 00:04:26,490 --> 00:04:32,760 that we have calculated during Tusk Space Trajectory Planning Director to join us because we have to 60 00:04:32,760 --> 00:04:36,390 convert them into joint space coordinates that joints can understand. 61 00:04:36,870 --> 00:04:43,200 And as you know, this process includes inverse kinematic step, and we have to do that at each step. 62 00:04:43,860 --> 00:04:50,160 You also know that calculating inverse kinematics is painful, so execution of task space trajectory 63 00:04:50,160 --> 00:04:57,270 is slower than Joint Space Trajectory because during planning trajectory in joint space, we obtain 64 00:04:57,270 --> 00:04:59,550 joint space coordinates and we don't need to. 65 00:05:00,180 --> 00:05:06,870 The metrics, in order to feed these coordinates into the joint, so execution of joint space trajectories 66 00:05:06,870 --> 00:05:07,560 is faster. 67 00:05:08,050 --> 00:05:14,070 Additionally, we have advantage of taking into consideration of singularities during planning trajectories 68 00:05:14,070 --> 00:05:15,000 in joint space. 69 00:05:15,360 --> 00:05:21,360 Moreover, joint space trajectories are smoother than thrust space coordinates because we directly control 70 00:05:21,360 --> 00:05:22,230 the actuators. 71 00:05:22,590 --> 00:05:28,770 Another problem with joint space trajectory planning is we cannot ensure that the planned trajectory 72 00:05:28,770 --> 00:05:31,260 is collision free and the behavior of the end. 73 00:05:31,260 --> 00:05:36,960 The vector is predictable because we control actuators, but we don't know what's happening with the 74 00:05:36,960 --> 00:05:39,360 motion of the end effector in the task space. 75 00:05:39,930 --> 00:05:46,560 This is not the case in past space trajectory planning because we directly see that what is our trajectory 76 00:05:46,560 --> 00:05:47,540 in task space? 77 00:05:48,120 --> 00:05:50,880 That's all about introduction to trajectory planning. 78 00:05:51,180 --> 00:05:52,620 See you on the next lesson.