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Instructor (Oussama Khatib):Okay. Let’s get started. Welcome to intro to robotics 2008. Happy new year, everyone. In introduction to robotics, we are going to really cover the foundations of robotics. That is, we are going to look at mathematical models that represent robotic systems in many different ways. In fact, you just saw a simulation of a humanoid robotic system that we are controlling at the same time. If you think about a model that you are going to use for the simulation, you need to represent the kinematics of the system. You need also to be able to actuate the system by going to the motors and finding the right torques to make the robot move.

Here is a robot you would like to control. The question is how can we really come up with a way of controlling the hands to move from one location to another? If you think about this problem, there are many different ways of controlling the robot. First of all, you need to know where the robot is, and to know where the robot is, you need some sensors. What kind of sensors would you have on the robot to know where the robot is? GPS? Okay. How many parameters can you measure with GPS? We can try that.

What can you determine with GPS? You will locate X and Y for the location of the GPS. But how many bodies are moving here? When I’m moving this here, how many [inaudible] are moving? How many GPS systems do you want to put on the robot? We would need about 47 if you have 47 degrees of freedom, and that would be too expensive. Another idea? Encoders. Encoders measure one degree of freedom, just like the angle, and how many encoders would we need for 47 degrees of freedom? Forty-seven.

That will give you the relative position, but you will not know whether this configuration is here or here. You need a GPS to locate one object and then locate everything with respect to it. Any other ideas? By integrating from an initial known position or using vision systems to locate at least one or two objects. Then you know where the robot is. The relative position – the velocities could be determined as we move.

Once we located the robot, then we need to somehow find a way to describe where things are. Where is the right hand? Where is the left hand? What do you need there? You need to find the relationship between all these [inaudible] bodies so that once the robot is standing, you know where the arm is positioned and where the hand is positioned. You need something that comes from the science of – I’m not talking now about sensors.

We know the information. We need to determine a model – the kinematics model. When the thing is moving, it generates dynamics. You need to find inertial forces. You need to know if you move the right hand, everything is moving. You have a coupling between these rigid bodies that are connected. You need to find the dynamics.

Once you have all these models, then you need to think about a way to control the robot. How do you control a robot like this? Let’s say I would like to move this to here. How can we do that? Very good. The forward kinematics gives you the location of the hand. The inverse kinematics gives you given a position for the hand that you desire. You will be able to solve what [inaudible] angles you have. If you do that, then you know your goal position angle for each of the joints. Then you can control these joints to move to the appropriate joint position and the arm will move to that configuration.

Can you do inverse kinematics for this robot?

Here is a robot you would like to control. The question is how can we really come up with a way of controlling the hands to move from one location to another? If you think about this problem, there are many different ways of controlling the robot. First of all, you need to know where the robot is, and to know where the robot is, you need some sensors. What kind of sensors would you have on the robot to know where the robot is? GPS? Okay. How many parameters can you measure with GPS? We can try that.

What can you determine with GPS? You will locate X and Y for the location of the GPS. But how many bodies are moving here? When I’m moving this here, how many [inaudible] are moving? How many GPS systems do you want to put on the robot? We would need about 47 if you have 47 degrees of freedom, and that would be too expensive. Another idea? Encoders. Encoders measure one degree of freedom, just like the angle, and how many encoders would we need for 47 degrees of freedom? Forty-seven.

That will give you the relative position, but you will not know whether this configuration is here or here. You need a GPS to locate one object and then locate everything with respect to it. Any other ideas? By integrating from an initial known position or using vision systems to locate at least one or two objects. Then you know where the robot is. The relative position – the velocities could be determined as we move.

Once we located the robot, then we need to somehow find a way to describe where things are. Where is the right hand? Where is the left hand? What do you need there? You need to find the relationship between all these [inaudible] bodies so that once the robot is standing, you know where the arm is positioned and where the hand is positioned. You need something that comes from the science of – I’m not talking now about sensors.

We know the information. We need to determine a model – the kinematics model. When the thing is moving, it generates dynamics. You need to find inertial forces. You need to know if you move the right hand, everything is moving. You have a coupling between these rigid bodies that are connected. You need to find the dynamics.

Once you have all these models, then you need to think about a way to control the robot. How do you control a robot like this? Let’s say I would like to move this to here. How can we do that? Very good. The forward kinematics gives you the location of the hand. The inverse kinematics gives you given a position for the hand that you desire. You will be able to solve what [inaudible] angles you have. If you do that, then you know your goal position angle for each of the joints. Then you can control these joints to move to the appropriate joint position and the arm will move to that configuration.

Can you do inverse kinematics for this robot?

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