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For a nonholonomic system, you can at best determine a differential relationship between state and inputs. You cannot determine a closed-form geometric relationship. This means that the history of states is needed in order to determine the current state. Vehicles are a good example because you can intuitively see that turning the right wheel 100 ...


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In that context, SE means "Special Euclidean" group, e.g. SE(3)* which is shorthand for "the special Euclidean group of rigid body displacements in three-dimensions". *Planning Algorithms, Steven M LaValle 2012-04-20


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A holonomic constraint is a constraint on configuration: it says there are places you cannot go. That is a reduction in freedoms. That’s (usually) bad. A nonholonomic constraint is a constraint on velocity: there are directions you cannot go. But you can still get wherever you want. That’s (usually) good! Ref: Mechanics of Manipulation by Mathew T. Mason


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Scott-Russell type mechanism. For weeks I was trying to come up with a solution for that exact problem for a engineering project mine. Look it up.


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Robots tend to be portable devices powered by batteries. Portable battery operated devices tend to use embedded processors with limited power and memory. Compiled code has several advantages over interpreted code in such applications: Compiled code usually takes up less space. So you can have more code in the same amount of space. Compiled code usually ...


4

Since the problem is one dimensional, you are actually asking to compute a velocity profile. (A velocity profile is the information of how a path is traversed with respect to time.) Now the problem is "How to travel for $B$ units within time $T$?" (Let's call the duration $T$ instead.) A velocity profile can be viewed as a curve in the $v$-$t$ (velocity vs ...


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It is a mathematical concept call the "Special Euclidean" group. Roughly, it is a combination of a rotation and translation. You'll also frequently see SO3, which is the special orthogonal group which means rotations.


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$SE(3)$ is the representation for both translation and rotation in 3D space, whereas $SO(3)$ is only the representation for rotations. $\mathbb{R}^3$ is for translations in 3D space. If you only consider 2-dimentional space, then you can simply change 3 to 2, i.e., $SE(2)$, $SO(2)$, $\mathbb{R}^2$. I wouldn't worry too much about it. You can just consider ...


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Holonomic constraints are constraints that can be expressed in the form of an equation relating the coordinate of the system and time Non-holonomic are constraints that cannot be expressed in the form of equations but it is expressed in the form of inequality.


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This is just basic trigonometry; you'll covert your world-relative calculations of roll and pitch ($\phi$ and $\theta$) into vehicle-relative values, based on yaw ($\psi$). Just so we're on the same page, I'm assuming measurements like the following, with roll, pitch, and yaw being zero when levelly flying North: $$\phi_{vehicle} = \phi_{world}\cos(\psi) - ...


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This is called a Stewart platform. You can use any linear actuator type, hydraulic, pneumatic or electric.


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This should have probably been a comment to @RobertEnglish answer ... but comments don't seem to allow pictures Bavel gears. Plastic ones should be rather inexpensive.


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Hmm, thats definitely a unique idea. I think the shape of the top gear would have to be rounded off like half of a torus so it maintains a good interlocking through the motion from parallel to 90 degrees. Also, the motion that the top shaft/gear go through during that transition might not be a simple rotation...it might be a rotation + translation. I'm just ...


2

There are far too many to list them all here but I can list the most common ones: As you said base the movement off the motor RPM, and the diameter of the wheels and move for a period of time. This is not normally very accurate and can result in the robot "leaning" one way or another. Use potentiometers to directly measure the wheel rotation and bring the ...


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My solution is to use the following model with disturbance only at acceleration and curvature. $$ \begin{bmatrix} x_{k+1} \\ y_{k+1} \\ \theta_{k+1} \\ v_{k+1} \\ a_{k+1} \\ \kappa_{k+1} \\ \end{bmatrix} = f_k(\vec{x}_k,u_k,\vec{\omega}_k,\Delta t) = \begin{bmatrix} x_k + v_k \Delta t \cos \theta_k \\ ...


2

If I understand you right, you want to achieve that three roombas clean 24 hours a day, just making a break if they need to recharge and then continue. The Create 2 is a roomba robot that is similar to the 600-series, but some article says it can not clean, which is good as this saves the energy that would be needed to drive the vaccum and brush motors. This ...


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It looks (to me) like there's a typo in that answer. The approach is to recognize that you have to wind up at the same point, whether you get there via the left arm (d->e->blue dot) or the right arm (a->b->c->blue dot). This means that you can go: $$ \Sigma_{x_{\mbox{left arm}}} = \Sigma_{x_{\mbox{right arm}}} \\ \Sigma_{y_{\mbox{left arm}}} = \Sigma_{y_{\...


2

Not sure how you're choosing to structure your code, but typically I'll have a master reference, in percent, and a rate limit, in percent per second. You can have different rates for acceleration or deceleration, but I'll post a generic snippet that uses the same rate limit for both. In the code, the master reference is the unramped (typically square) ...


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I think this is just a way of illustrating the main idea behind the probability distribution and the representation is not complete. The idea is that there is a moment when the door is detected and the prior distribution not yet considered, this is when the robot assumes this could also be door 1 and therefore the positions of the other doors are as shown. ...


2

The robot has sensed a door, so the initial belief distribution matches the three possible door positions. i.e. the only three places that it is possible for the robot to be in that scenario. The robot moves to the right so, since the belief distribution matches the possible positions of the robot, the belief distribution must also move to the right. As the ...


2

Here is what I 'believe'. Lets make the diagram more labeled. Say door 1 starting from left most is at 4 meters from the origin at left, door 2 at 7 meters, door 3 at 15 meters. When the robot senses a measurement corresponding to a door it thinks that it has high and equal probability of standing in front of any of those doors and very low probability that ...


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A general approach would be to construct a so called axis-angle representation and convert that to a rotation matrix representation. On order to do so, one could start with a normal vector of the triangle. Let's take the $P_1P_2$ line and construct the perpendicular of the triangle from $P_3$ to $P_1P_2$. Let's call $P_4$ the point where the ...


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First of all you should start to check 2 things: the angle $\alpha$ is given by some sensor the object and the path to the object (blue dotted line) both lie in the arm workspace If 1. is not met, I suggest you to look in the literature of eye-in-hand servoing. If 2. is not met your object can not be reached ... you might still want to travel until the ...


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Many people use Python to control robots. While it does use more computing resources to interpret the python code, it may take less time for the programmer to develop in an interpreted language. Advantages of Python: Many programmers are familiar with Python because it is often taught as a first language in schools. It can be faster to program in Python ...


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There are 4 possibilities: One of the wheels' centre is displaced slightly. Wheel encoders are not properly positioned and this is causing issues (like wheel pausing at odd positions while microcontroller 'thinks' it has achieved the right position) One of the wheels' radius is lesser than the other one. As per @GurkanSetin 's comment, friction might be ...


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Lets suppose, that left wheel is blocked, so nMotorEncoder[LM] is constantly zero, while nMotorEncoder[RM] counts something. Correct behavior is for right motor to effectively stop (or jumping little back and forth the same lenght). Now LEncoder is 0, REncoder is negative, LEncoder > REncoder so motor[LM] = speed1 - difference; ...


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A constraint on the $k$ coordinates $r_1,r_2,...,r_k$ is holonomic if it is an equality constraint of the form $$g(r_1,...,r_k)=0,$$ and nonholonomic otherwise. These sorts of constraints arise frequently in mechanical systems (e.g. when deriving Euler-Lagrange equations of motion). A holonomic system is one that is subject to holonomic constraints, and a ...


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It sounds like you can estimate everything you need to with a direct calculation of the transform between each vehicle since that is provided for you. For the derivative parameters, if your sensors give direct measurement (velocity from doppler on the radar for instance) you probably want to use those values rather than filtering. Without knowing more I'd ...


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Well, I moved my answer here from the Engineering SE because it looks like your question is probably going to get closed there, just like it got closed at the physics site. Assuming everything about the vehicles is the same - mass especially, but also shape, center of gravity, etc., such that the entire problem boils down to tire grip, you will lose. See ...


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Well the IR tracking system can work, but I think you need to place the camera at the ceiling. Usually the distance between player and camera at the ceiling of a tennis-hall (height 8+m I guess) stays about the same. Using IMU-Data is a bad idea cause of the really complex movement EDIT1: For implementing the IR-Tracking (in this case a pretty simple one) ...


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