Advanced Robotics

Every robot that is under servo control requires a kinematic engine in order to compute the control parameters that are passed to the actuators which provide the motion. This particular robot had 9 degrees of freedom. This kinematics engine (that I wrote) used an iterative solver because the orientation degrees of freedom (aka the wrist) did not have their axis of motion intersect at a single point (Pieper 1968).

The solver took me a calendar year of development. It was improved from 1 second per path point prototype written in Sil to 100 nanoseconds per path point written in C++ including full redundancy. All Fanuc paint robots use the Hadi Akeel wrist (named after the VP of Engineering at Fanuc who designed and patented it) which has 3 concentric torque tubes driving the ring gear which provided motion. This allowed some symmetry considerations to be exploited to make the solver faster. It was not a completely generic solver so it would not work for many other kinematic found in the paint robot world.

I read Dinesh Manocha’s PhD thesis (Cal Berkely) looking for a general solver. He used the multipolynomial resultant technique to provide solutions for generalized six degree of freedom robots, and as most industrial robots are 6 degree of freedom devices this might have wide applicability. At the time this technique was not suitable for real time devices because the convergence would not meet the 100 nanosecond requirement of my real time system (30 seconds on the IBM 370). His technique was a special case of the more general technique of solving systems of polynomial equations using homotopy and analytic continuation. Dr. Wampler’s Homotopy method is the most rigorous algorithm available. The solution set will also provide all available manifolds for a given data set.

Dr. Charles Wampler (GMR, Notre Dame) has published his work in homotopy and analytic continuation for kinematics.

I am currently developing the “generic” 6 DOF solver using the GNU Scientific Library and Dr. Wampler’s homotopy method. If it is fast enough on cheap hardware (2Ghz $300 PC) I will port it to the Microsoft Robotics Studio. Dr. Wampler’s book is an excellent introduction to the kinematics of novel devices like those seen on the cover above.

The best book I have read on industrial robotics is the “Bible” by Dr. Richard (Lou) Paul.

The LARPS robot was largely built by turning to page 1 chapter 1 and getting started. This book is now out of print but you can find used copies at Amazon. If you work your way through this book you will learn all that is needed to build a robot and control system, you will also fix more than a few typos/math errors but that is half the fun! A more popular version of this is John Craig’s book. John, Ric, and Paul (Silma) consulted on the LARPS project assisting with the simulation environment and optical TCP algorithm.

There are many other books on robot engineering (many imitators) but for an excellent survey these are the best.

Dr. Paul was issued a patent for an algorithm in path planning in 1997. We had already implemented this algorithm in the LARPS system, sorry dude. We used it for approach/departure control and to find hidden singularities on linear trajectories for the full and redundant 9 DOF system.