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Why in trajectory planning in joint space the manipulator never crosses a singularity?

The term "singularity" characterizes those configurations in the joint space where the Jacobian matrix loses rank and thus it is not directly invertible. The Jacobian, in turn, is used to remap a ...
Ugo Pattacini's user avatar
4 votes
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Motion profile and Motion control scheme, how do they interact?

These two concepts are complementary and you use them together, the motion profile providing the input to your control scheme. At each time-step the motion profile gives you the reference values for ...
50k4's user avatar
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3 votes
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My Pick and Place Program Not Working

The best way to debug geometry related applications is by using plots. First of all, plot the initial configuration, with robot TCP, cube initial position, cube final position. As these are all input ...
50k4's user avatar
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3 votes
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SLERP velocity and acceleration (3d Orientation interpolation)

Derivative of $\sin$ is $\cos$, and the derivative of $\cos$ is $-sin$. Given a quaternion definition of: $q = \cos{a} + \mathbf{r}\sin{a}$ $\mathbf{r}^2 = -1$ I would expect to see what is ...
Chuck's user avatar
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3 votes
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where can I find a good source to study robotics kinematics and trajectory planning relative to robotic arm manipulator?

Here is my main source, take a look at this book : Craig, John. J. (2005). Introduction to Robotic : Mechanics and Control. Pearson Education Inc. Corke, Peter P. (2017). Robotics, Vision and Control....
Albert H M's user avatar
3 votes
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How do I find the minimum time for computing a trajecotry for a robotic arm?

Your problem statement is: using a bang-coast-bang acceleration profile with symmetric acceleration and deceleration phases, each of duration $T_s=\frac{T}{4}$. So, right off, you know the time ...
Chuck's user avatar
  • 16k
3 votes

Iterative calculation of trajectory

Trapezoidal trajectory is basically a piecewise quadratic function. Since the function is quadratic, its second derivative is a constant. The trajectory is then basically comprises segments of ...
Petch Puttichai's user avatar
2 votes
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Given an initial position, a goal position and a duration find a trajectory

Your pseudocode seems to do what you expect but it is not up to the task at hand since the approach of doing path planning in velocity is fundamentally wrong. Instead, you should be doing path ...
Ugo Pattacini's user avatar
2 votes

What is a cost and cost function in path planning?

The term cost function in path planning is borrowed from optimization. Rightfully so, since path planning in most cases is, in fact, an optimization problem. The cost function in optimization ...
50k4's user avatar
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2 votes
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Trajectory generation equation from jacobian and inverse kinematics

As suggested by ben, i will put my comment as answer. 1st How to control robot I recommend you to look about resolved motion rate control. It's a complete algorithm to control a robot from path ...
Albert H M's user avatar
2 votes
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How to estimate gradient of Jerk

The code is computing the gradient of the cost, which is jerk squared, not the gradient of the jerk. The comment there is misleading! As written, it seems the code is implementing the chain rule of $$ ...
Alex's user avatar
  • 449
2 votes

how the two equatoin are linearized

Consider the formula for the linearization of a function $f(\mathbf{x})$ about a point $\mathbf{x}_{e}$, where $\mathbf{x}, \mathbf{x}_{e} \in \mathbb{R}^{n}$: $$f(\mathbf{x}) \approx f(\mathbf{x}_{e})...
domo_arigato's user avatar
2 votes
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Why is a joint space trajectory unable to deal with operational space obstacles?

The main difference between task space control and joint space control are : Joint space : You know start and last position of joint configuration from IK(Inverse kinematic), and interpolate it Task ...
Albert H M's user avatar
2 votes
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Problem designing acceleration inputs controller

You've been asking lots of questions along these lines, and I've been there before - I know what it is to be at your wits end trying to find a solution. I'm going to try to help, but part of my "...
Chuck's user avatar
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2 votes

Rigorous terminology clarification - Path Planning, Path Following, Trajectory Planning, Trajectory Following and Motion Planning

Well I think you got it right for the differentiation. Path planning is about generating a path, that is not related to time. The planning algorithm may take into account some holonomic constraints, ...
oKermorgant's user avatar
1 vote

Designing S-Curve velocity profile for given Distance

You were probably trying to avoid this and generate some kind of closed form solution, but as you show this is really burdensome. They way I would solve this (which might not be the best way) would be ...
guero64's user avatar
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1 vote

Matlab smooth transition between stored configurations (rigid body tree robot )

I don't know how you're storing or recalling your presets, but you can put a Rate Limiter block between it and your joint and limit how quickly your joint reference changes. I made a short clip for ...
Chuck's user avatar
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1 vote

Is there any need to guarantee the duration of one planned trajectory is an integer times rather than a decimal times of interpolation period Ti

You're mentioning a period without going into any detail about it, so I'm not positive what you're asking about, but I'm guessing your concern is about a computation period - the inverse of the ...
Chuck's user avatar
  • 16k
1 vote

How to design a PID controller for boat?

It should be perfectly fine to control the boat with two thrusters (i.e. propellers with some distance in between them), via a PID control scheme. To compensate for ambiguities in the model and the ...
Gürkan Çetin's user avatar
1 vote

Relative scale problem

Does inliers and outliers have something to do with this problem? -> Yes, your odometry estimation error will be accumulated in the point cloud and it will eventually end up what you are ...
Chanoh Park's user avatar
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1 vote
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How to investigate the relation between planning frequency and control response?

On the theory side, this is related to the Nyquist Sampling Rate, which is how frequently you must measure a single to get an accurate reconstruction of it's peaks / valleys. Not suprisingly, Nyquist ...
Josh Vander Hook's user avatar
1 vote

Generate a Trajectory from GPS coordinates

Extending the previous answer which describes how to compute a minimum-jerk trajectory given a consistent distance coordinate system. A simple way to do this is to treat the first coordinate as your ...
Octopuscabbage's user avatar
1 vote

Generate a Trajectory from GPS coordinates

As reported for example in https://robotics.stackexchange.com/a/21571/6941, a minimum-jerk trajectory in one dimension is coded with respect to time $t$ as: $$ x(t) = x_i + (x_f-x_i) \cdot \left( 10\...
Ugo Pattacini's user avatar
1 vote
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Sinusoidal trajectory of each cartesian coordinate for the end effector

The short answer is yes, it is possible. The long answer is: The all xyz coordinates have to be inside workspace boundaries of the robot Solving IK for 7 DOF is a bit harder then any other non ...
50k4's user avatar
  • 6,682
1 vote

Trajectory planning in unstructured environments

Short answer: At first, a motion capture recording of the robot is created. Secondly, the recording is converted into a task model. Long answer: A human operator is the natural source for providing ...
Manuel Rodriguez's user avatar
1 vote

Trajectory planning in unstructured environments

In general, you want to build a 3D map of the environment, or more likely an approximation of a 3D map. Typically such maps are grid-based across the horizontal plane, and each cell contains some ...
badmistersquirrel's user avatar
1 vote

Compute orientation velocities 6-DOF robot

I was able to figure out after digging further through several other posts and google searches. This post pointed me in the right direction: https://physics.stackexchange.com/questions/293037/how-to-...
Lucas's user avatar
  • 21
1 vote

SLERP velocity and acceleration (3d Orientation interpolation)

I think you may have a mistake in python code. That is: slerp_d = slerp * np.log(qf * q0.inverse()) I think the correct one is: ...
mingjun han's user avatar
1 vote
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how do I decide what is the order of the polynomial I need to use in a polynomial iterpolation for a trajectory?

This sounds exactly like cam design. When designing a cam profile, you typically want the cam follower to be at certain displacements at certain times, and you can usually choose how it gets there. ...
Ben's user avatar
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1 vote

Reset coordinate system of robot while maintaining relationship to the previous

Instead of just considering it a reset, you should consider it a coordinate system transformation: You set the position to zero, that means that you create a transformation matrix which brings your ...
50k4's user avatar
  • 6,682

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