The function $f$ comes from the equation of motion for the inverted pendulum problem (inverted pendulum alone, not including the motion of the wheeled platform). If you consider your figure but ignore ...

Both the forward kinematics and inverse kinematics aren't too difficult, but always a little tricky for parallel manipulators like this one. Consider the configuration in this diagram. The forward ...

You are most likely running into problems with the maximum time step in your simulation. This phenomenon is known as stiffness, where your equations of motion are highly sensitive to the size of the ...

Actually, the caster wheel has ideally no effect on the kinematics of the vehicle. In reality there will be some resistance from the caster wheel that does impact the vehicle motion, but we can still ...

Your question might be better suited to another forum, but is definitely important for robotics in general. You are basically talking about unstable equilibrium, where there does exist a point where ...

The torque bandwidth is typically referring to the maximum frequency of motion at which the actuator can provide that torque. So your actuator can provide a peak torque of 100 Nm, as in it can hold up ...

The actual implementation of SLAM won't care about whether you are using high fidelity laser range finders or cheaper ultrasonic sensors. Both are providing range measurements with the biggest ...

You should simply use the callback method since you can have an object in your code that is always updated with the latest measurement. Then you can simply poll the measurement in that object whenever ...

In general, Euler angles (or specifically roll-pitch-yaw angles) can be extracted from any rotation matrix, regardless of how many rotations were used to generate it. For a typical x-y-z rotation ...

Your motors do not develop the thrust, they spin rotors which develop thrust. Practically speaking, it is probably better to create an empirical model (or look-up table) based on measurements of the ...

I think your diagram is missing an angle for the laser angle with respect to the vehicle body -- I'm going to call that angle $\alpha$, see this diagram for clarity: Since it seems you are tracking ...

There isn't really a difference. "Path planning" might be used more often to simply describe the problem of finding a desired path from one state (or sub-set of states) to another. Whereas "motion ...

The gyroscope placement shouldn't make any difference since the rotation rate will be the same everywhere (assuming your robot is rigid enough). The accelerometer will pick up the rigid body ...

Statistical confidence is most often defined in terms of a score that is the number of standard deviations away from the mean. Now let's say you have a set of states (a state vector) used to define ...

There is an error in your posted equation for the Jacobian $F_J$, so that could be the source of the problem. It should look like this: $F_J = \begin{bmatrix} 1 & 0 & -C \sin \theta \\ C \... View answer 2 votes The problem you want to solve is definitely a SLAM problem and not just simply localization (or maybe we can consider it SLAm since the mapping part is not as heavy). The reason for this is that you ... View answer 2 votes This already happens when a commercial robot product comes off of the assembly line! The robot software is the same for each robot and is copied over. Some robots work using similar computer ... View answer Accepted answer 2 votes The linkages suggested by jwpat7 are great, and I would probably prefer to use something like that. But, if you want something really simple, then you might be able to get away with a four-bar linkage ... View answer 2 votes Kinematic decoupling really depends on the configuration of your particular manipulator. When you decouple the wrist, it is typically so that you can take any given end-effector pose and determine the ... View answer Accepted answer 2 votes The critical part is the registration between depth data and RGB data. If the registration is calibrated properly then you can just extract the depth for the particular target pixel (X,Y), using ... View answer Accepted answer 2 votes Here are my two suggestions for dealing with this problem: Use a median filter, which replaces each value of your signal with the median of the values in a small window around each one. Here is some ... View answer 2 votes The inverted pendulum is unstable in the sense that it will diverge away from the upright position if perturbed (for example, slightly blown by wind or lightly vibrated). On the other hand the "... View answer 2 votes It sounds like you are developing a robotic manipulator from scratch so I also assume you will be writing software for position control too. Both the design and control depend on not only the dynamics ... View answer Accepted answer 2 votes The main differences between brushed and brushless DC motors are cost, efficiency, and complexity. Brushless motors don't have brushes (surprise!) so they don't wear down as fast as brushed motors and ... View answer Accepted answer 1 votes Surface properties like that are really only for cosmetic purposes so it is unlikely any CAD program has that option. However, you may be able to get the appropriate effect by assigning particular ... View answer 1 votes Most gear motors with integrated encoders have them placed on the motor shaft, which allows for much finer angle resolution at the output but does not account for backlash. I think this is what you ... View answer Accepted answer 1 votes Image features are connected to the camera pose through two steps: (1) the relationship between the feature pixel coordinates and its homogeneous coordinates in the camera reference frame, and (2) the ... View answer Accepted answer 1 votes Applying the rotation sequence (x-y-z) that you specify, your first robot tool will have the following rotation matrix:$R_1 = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 &...

For a heating element you want lower resistance -- remember $V = I R$, so high resistance means lower current, and that in turn means lower power for the same applied voltage since $P = \frac{V^2}{R}$....
Overall, you simply need to rotate each point in your cloud using the rotation matrix $R$. That rotation matrix will be the latest rotation matrix for your vehicle/sensor. You can compute the rotation ...