# Questions tagged [trajectory]

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### Combining dynamic movement primitives to create new ones

this is my very first question and I want to thank everyone for the massive contribution to the community! On to my question now, here is a quick definition of my idea/problem: I have created a "...
82 views

### how the two equatoin are linearized

corresponding paper Question1: how the equatoin 3 is linearized in the neighborhood of the equilibrium point $x = x_{sp}, \dot x =0$ Question2: how the equatoin 12 is linearized in the neighborhood ...
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### Suggestion for path following algorithm for mecanum wheeled mobile robot

I have a robot with four Mecanum wheels. I want to make robot follow different paths. The path information is given in x,y coordinates. I want to start from simplest controller i.e. open loop type as ...
23 views

I have defined a quadcopter that I control with a PID controller. The dynamics that define it are such. $T=mg+m\ddot{z}$ $\theta=\frac{\ddot{x}}{-9.82}$ $\phi=\frac{\ddot{y}}{9.82}$ As you can see I ...
79 views

### Joint space trajectory script unclear

I have a script provided by The MathWorks Inc. that makes a robot end-effector follow both a task space and a joint space trajectory through several waypoints. These trajectories are then plotted in ...
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### Decidability of Pursuit-Evasion games and self driving cars

I was wondering if there is any theory describing the decidability of a continuous pursuit-evasion game with constraints. Scenario: Two cars approach each other on a street with two lanes. Let's say ...
1 vote
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### Why is a joint space trajectory unable to deal with operational space obstacles?

I have found several sources that state that a Joint space trajectory model is not capable of dealing with obstacles in the manipulator workspace. These sources include: slide 10 of "Manipulator ...
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### Matlab smooth transition between stored configurations (rigid body tree robot )

I currently have a few joint configurations stored for a robot model in Matlab. When I play back and show the robot in different configurations, there is of course no smooth, but abrupt transition. Is ...
36 views

### 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

Take double S of velocity profile for example where the seven segments exist. Given the desired displacement s, the constraints ...
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### How to design a PID controller for boat?

I have a boat with two trusters and a trajectory planner which is based on the bicycle model. In order to control the boat, the linear velocity of each truster has to be provided. The following ...
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### Relative scale problem

I am doing Monocular Visual Odometry, and I have problem with relative scale. Most of the time its value is between 0.8-1.1, but sometimes it goes crazy and it has value 3,4 and once it had value 25. ...
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### How to investigate the relation between planning frequency and control response?

I have a speed control system which is part of a hierarchical planning and control stack. The final output of this system is torque and the input is desired speed. The system is experiencing some ...
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1 vote
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I'm currently following a course on coursera on quadrotors, and i'm currently focusing on the trajectory planning mechanism. In the course, it's said that one of the criterias when planning a ...
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### Trajectory generation equation from jacobian and inverse kinematics

I just built a 4 DOF Articulated manipulator with open-loop servo motors and the servos signals are generated using a micro-controller. I followed the Angela Sodemann's videos on YouTube, I calculated ...
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1 vote
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### How to estimate gradient of Jerk

A trajectory is described by a position vector, i.e., traj = $[q_0, q_1,...,q_n]$. The objective is to minimize the jerk of the trajectory. I am referring to this code to understand how the gradient ...
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### Generate a Trajectory from GPS coordinates

How would I generate a trajectory (e.g. minimum snap/jerk/acceleration) for a quad rotor between GPS coordinates? In all the examples that I have seen, they assume that the x,y positions are in meters ...
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1 vote
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### Can I relate trajectory generation to differential inverse kinematics?

I am wondering how (if) one can translate trajectories of translation matrices to joint velocities? I'm reading the notes of Russ Tedrake's class on manipulation. One part of the notes concerns a ...
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### Sinusoidal trajectory of each cartesian coordinate for the end effector

Consider a 7-DOF robotic manipulator. I want the end effector to follow a predefined trajectory and suppose I care only about the position and not about the orientation. So, the rotation part of the ...
74 views

### Problem designing acceleration inputs controller

I am reading this paper: https://www.researchgate.net/publication/224635390_The_motion_control_problem_for_the_CyberCarpet in which is implemented a cartesian regulator to bring the position $(x,y)$ ...
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### Motion profile and Motion control scheme, how do they interact?

I'm studying motion control and I start with the simplest case, I have to go from A to B in a straight line using a trapezoidal motion profile. I understand that in a real case, due to the fact that ...
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### Trajectory planning in unstructured environments

How is trajectory planning normally carried out in off-road/unstructured environments? In particular I'm interested in how stereo vision can be used to plot trajectories over obstacles - for example, ...
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1 vote
60 views

### My Pick and Place Program Not Working

hope you are all well. I am trying to finish a capstone project on Coursera. It asks me to carry a cube object from an initial position to goal. This video shows the movement. Project website: http://...
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1 vote
167 views

### Compute orientation velocities 6-DOF robot

I am trying to compute the joint velocities a 6-DOF manipulator(a typical industrial robot). I have an initial position [xi, yi, zi, T1i, T2i, T3i] and goal position [xf, yf, zf, T1f, T2f, T3f] in the ...
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### What is a cost and cost function in path planning?

Surfing through websites and videos, I interpreted that cost refers to parameters such as time taken to go from start position to the goal position or distance traveled in every possible path and cost ...
408 views

### SLERP velocity and acceleration (3d Orientation interpolation)

Hey guys I am quite new to quaternions and I am a bit unsure as to how to use them. How are the velocities and accelerations trajectories determined using quaternions? I have been using slerp to ...
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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?

I am a student studying robotics, and I am focusing on trajectory planning for a robotic arm. In particular, I am studying polynomial interpolation for defining the trajectories, and I am having some ...
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### How do I find the minimum time for computing a trajecotry for a robotic arm?

I am studying robotics and I am focusing on trajectory planning. I have been struggling with this topic for a while, and I still have some doubts that I cannot solve. One of them is the following: I ...
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1 vote
94 views

### Reset coordinate system of robot while maintaining relationship to the previous

I am currently estimating a robot's pose (3d position and rotation matrix) with an IMU and I want to reset the localizer in the middle of the run while keeping the relationship to the pose it had when ...
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### where can I find a good source to study robotics kinematics and trajectory planning relative to robotic arm manipulator?

I am a student, and I have to study for a Robotics exam which consistes mainly in kinematics for a robotic manipulator and trajectory planning also for a robotic manipulator. In the part relative to ...
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### Going from Spline to Differential Drive Command

I have a differential drive robot that needs to move along a path stored in its memory as a spline. I am currently trying to understand the mathematics of determining how much power to apply to each ...
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### Why in trajectory planning in joint space the manipulator never crosses a singularity?

I am studying robotics kinematics and I have studied that if we plan a trajectory in joint space it is impossible for the robot manipulator to cross a singularity during its motion, while in cartesian ...
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### Trajectory tolerance limits

I have a trajectory planner, which calculates the trajectory assuming that the robot is following the planned trajectory. From sensors I get the position of the robot, which has an offset from the ...
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1 vote
1k views

### What are the differences between trajectory planning, trajectory tracking, path planning, path following and motion planning?

What are the differences between trajectory planning, trajectory tracking, path planning, path following and motion planning? And what are the basic methods they use?
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1 vote
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### Iterative calculation of trajectory

In the answer https://robotics.stackexchange.com/a/7512/22953 there is an example for trapetzoid trajectory planning that results in the following table. \begin{array} {|r|r|} \hline time &...
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### Given an initial position, a goal position and a duration find a trajectory

I have an initial position $X^R_{init}$ of the robot ($x$, $y$ and yaw) and a goal position $X^R_{goal}$ I need to create a trajectory of duration $T$ with $n$ waypoints to move the robot from its ...
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