FourBars_pendulum.world File Reference

Introduction

A planar four bar mechanism with dynamics.

The task consists in lifting a heavy load with a four-bar robot with a torque-limited actuator. By accounting for the robot dynamics and torque limitations at the planning stage, we take advantage of gravity, inertia, and centripetal forces to extend the motion capabilities of the robot.

Start Goal
[Model Parameters][Problem Dimensions][Process and Results]


Model Parameters

The robot involves four links cyclically connected with revolute joints from which only joint $J1$ is actuated. The relative angle with the following link is denoted by $q_i$, and the robot configuration is then given by ${q} = (q_1,q_2,q_3,q_4)$.

The lenght of the links are set to

$L_0$ 0.5
$L_1$ 1.0
$L_2$ 1.1
$L_3$ 1.0

The remaining set of geometric and dynamic parameters, such as mass, inertia or friction, are given within the world file accessible at the bottom of the page.

Problem Dimensions

The dimensions of the problem are

Nbr. of joints 4
Nbr. of states 8
Nbr. of actuators 1
Nbr. of position equations 3
Nbr. of position and velocity equations 6
State-space manifold dimension 2

Process and Results

This example is used to visualise the results of the kinodynamic planner.

First, to plot the state space manifold, follow these steps (from the main CuikSuite folder):

  • Create an atlas of the state space manifold:
  • Plot a 3d projection (dimension 0, 5 and 6) of the atlas:
  • Visualize:
    • geomview examples/FourBars/FourBars_pendulum_atlas_triang.gcl

Now, to solve the kinodynamic planning problem, follow these steps (from the main CuikSuite folder):

  • Run the kinodynamic RRT algorithm:
  • Plot a 3d projection (dimension 0, 5 and 6) of the RRT :
  • Visualize the solutions:
    • geomview examples/FourBars/FourBars_pendulum_atlas_triang.gcl examples/FourBars/FourBars_pendulum_atlas.gcl FourBars_pendulum_rrt.gcl

  • Execute the trajectory:
    • scripts/cuikplayer examples/FourBars/FourBars_pendulum examples/FourBars/FourBars_pendulum_traj


Definition in file FourBars_pendulum.world.