Research
My
research is on the subject of control to enable a robot to free-climb via
real-time convex optimization. Previous research
on climbing robots has focused on robots that climb using specialized end
effectors (such as suction cups or magnets) or robots that climb by exploiting
features of their environment (such as robots that climb in tubes or on surfaces
such as trusses or chain link fences). In contrast, my research hopes to
enable climbing in irregular environments using friction properties of the
environment. Such ability would be useful not only in terrestrial search
and rescue, but also in exploration of steep surfaces on other planets such
as crater walls on the moon and Mars.
My research builds from previous research 
done
in the Aerospace
Robotics Lab by Tim Bretl.
He developed a method to plan the path of a climbing robot up an artificial
rock wall for robots having a frictional contact on a surface. He then demonstrated
the effectiveness of his path planning on JPL's
LEMUR IIb robot. A video
of LEMUR's climb (6 Mb) is available from Bretl's webpage. While the
plan for this climb was completely valid, LEMUR had some trouble in the execution.
The motion plan generated joint angle trajectories that LEMUR followed using
PD joint angle controllers. If large joint angle errors were detected, a
safety mechanism in the controller stopped the robot to reduce the possibility
of a fall. This happened fairly often and for a variety of reasons. Joint
motors saturated, hands slipped off holds, and holds were not in the locations
the surveyor described. Joint angle control does not have built in knowledge
of limitations and constraints imposed on the robot and also has no mechanism
to feed back the state of the robot with respect to these constraints.
To remedy these problems I have designed a controller called Cartesian Force, Convex (CFC) control that considers constraints on the robot and only generates torques that do not violate those constraints.
This controller has two key features:
- The controller tracks a planned trajectory by feeding back information about the robot CG position (x). The position of the CG of the robot is given by the motion planner and corresponds to a location at which it is possible for the robot to maintain equilibrium. Using a control technique such as PD control, a desired force on the CG is generated.
- Next, the desired force on the CG is achieved by using a convex optimization technique (such as linear programming). This ensures that the desired force is achieved without using torques that exceed torque limits or cause the hands to slip off of holds.
Additionally, given the many degrees of freedom for the climbing robots used in these studies, it may be possible to achieve more goals than those explicitly stated above. For example, I choose to minimize the norm of the joint torques for longer robot battery life, and also to minimize the angle of forces applied to holds with respect to the hold normal to increase robustness to hold angle and friction property errors.
I
have demonstrated the effectiveness of this controller on Stanford's Free-flyer
robots. These robots operate in a horizontal plane, but by hanging a weight
on a pulley over the edge of the table an artificial gravity environment
can be simulated. The figure on the right shows the robot climbing holds
that are in a chimney configuration. These holds are vertically oriented
so that the robot must not only push up to climb, but must also push out
just to keep its hands in the holds. The CFC can make this climb even in
the presence of hold position errors, whereas a joint angle controller is
unable to keep the robot from falling. A demonstration
video of this is available in Quicktime format.
This
controller has also been tested in simulations of JPL's LEMUR IIb robot.
The images at right show a position where the robot actually became stuck
while climbing because of an upper arm motor saturating. In the simulation
using CFC control, the robot was able to redistribute torque to other motors,
and with a lower arm helping push up LEMUR was able to complete the climb.
I hope to demonstrate CFC control's effectiveness on the actual LEMUR robot
in the near future. A major obstacle to this implementation is that LEMUR's
joints are highly geared and nearly completely non-backdrivable. This
is an appropriate design technique for climbing robots because if motor current
to the joints is set to zero, the robot doesn't move and battery life is
conserved. However, this makes control of joint torques and robot endpoint
forces very difficult without direct measurements of these values. (This
is opposed to the joints on the free-flyer robots which are direct drive,
so motor torque is proportional to current.)
My near term research will involve resolving the problem of controlling climbing robots with highly geared joint motors. I will be working with the robot built by Professor Jean-Claude Latombe as part of his climbing robotics research.
Further reading:
Climbing Robots
T. Bretl. Motion planning of multi-limbed robots subject to equlibrium constraints: The free-climbing robot problem. International Journal of Robotics Research, 25(3), 2006.
D. Bevly, S. Dubowsky, and C. Mavriodis. A simplifed cartesian computed torque controller and its application to an experimental climbing robot. Journal of Dynamic Systems, Measurement, and Control, 122(1):27-32, March 2000.
A. Shapiro, E. Rimon and S. Shoval. A foothold selection algorithm for spider robot locomotion in planar tunnel environments. International Journal of Robotics Research. 24(10):823-844, October 2005.
Convex Optimization Control Techniques
Y. Fujimoto and A. Kawamura. Simulation of an autonomous biped walking robot including environmental force interation. IEEE Robotics and Automation Magazine, pages 33-42, June 1998.
T. Schlegl, M. Buss, T. Omata and G. Schmidt. Fast dextrous regrasping with optimal contact forces and contact sensor-based impedance control. In Proc. of the IEEE International Conference on Robotics and Automation, pages 103-108, 2001.
Grasp Planning
I have also researched the issue of planning grasps on holds for rock climbing robots. Previous grasp planning research has focused on grasps that achieve force- or form-closure. Such grasps allow the gripper to subsequently pick up the object being grasped. A climbing robot does not need such a grasp to be able to climb.