The trajectory planner generates motion patterns based on two
specific concepts, being the use of objective locomotion
parameters, and exploiting the natural upper body dynamics by
manipulating the angular momentum equation. The
trajectories of the leg links, represented by 6th order
polynomials, are planned in such a way that the upper body motion
is naturally steered, meaning that in theory no ankle torque would
be required. Thus external disturbances are easily overcome and
the Zero Moment Point stays within the predefined stability
region. One of the most interesting aspects of this method is that
they are based on fast converging iteration loops, requiring only
a limited number of elementary calculations. The computation time
needed for generating feasible trajectories is low, which makes
this strategy useful for real-time applications.
More information about this subject can be found here.
Real time dynamic simulations
The dynamic simulation of complex mechanical systems is becoming increasingly important. Virtual prototyping provides strong optimalization tools and reduces overall cost and time-to-market. The goal of the research of Joris Naudet is the creation and implementation of a new recursive algorithm for the dynamic simulation of mechanical systems. The starting point is the use of canonical momenta to obtain a Hamiltonian formulation. The resulting algorithm seems to be more efficient than all known comparable algorithms.
This program shows the dynamic simulation of the robot Lucy. The program is compiled under Windows XP, using openGL (works for sure under Windows 2000 as well). THE FILE 'glut32.dll' IS NEEDED TO RUN THE PROGRAM!!! Put it in the 'windows/system32'-directory (or same directory as the application itself). In the near future, versions for other operating systems will be added.
- F1: Help
- F2: Toggle camera mode (free, follow Lucy)
- F4: Exit
- INSERT: toggle navigation mode ON/OFF
- ARROW KEYS: navigate
- MOUSE: move camera direction
- w: decrease step length
- x: increase step length
- q: decrease step height
- s: increase step height
- a: decraese step speed
- z: incraese step speed
Watch out: Do not change step mode too fast, this may lead to instability!
If this ever happens, just close the program and restart...
Animation of Lucy side view speed2.2 km/h, step length 0.3 m (avi 134 kB)
Animation of Lucy frontal view speed 2.2 km/h, step length 0.3 m (avi 270 kB)
Animation of Lucy stepping over an obstacle 2.2 km/h (avi 304 kB)
Animation of Lucy frontal stepping on a stairway. speed 1.8 km/h step length 0.3 m, step height 0.1 m (avi 376 kB)
Trajectory Generation for Planar Hopping and Walking Robots: An Objective Parameter and Angular Momentum Approach
Vrije Universiteit Brussel,