Certifying the safe design of a virtual fixture control algorithm for a surgical robot

We applied quantified differential-dynamic logic (QdL) to analyze a control algorithm designed to provide directional force feedback for a surgical robot. We identified problems with the algorithm, proved that it was in general unsafe, and described exactly what could go wrong. We then applied QdL to guide the development of a new algorithm that provides safe operation along with directional force feedback. Using \KeYmaeraD (a tool that mechanizes QdL), we created a machine-checked proof that guarantees the new algorithm is safe for all possible inputs.

[1]  André Platzer,et al.  KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description) , 2008, IJCAR.

[2]  André Platzer,et al.  Differential-algebraic Dynamic Logic for Differential-algebraic Programs , 2010, J. Log. Comput..

[3]  Russell H. Taylor,et al.  Constrained control for surgical assistant robots , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[4]  André Platzer,et al.  Quantified Differential Dynamic Logic for Distributed Hybrid Systems , 2010, CSL.

[5]  Peter Kazanzides,et al.  Proving the correctness of concurrent robot software , 2012, 2012 IEEE International Conference on Robotics and Automation.

[6]  Peter Kazanzides,et al.  An integrated system for planning, navigation and robotic assistance for skull base surgery , 2008, The international journal of medical robotics + computer assisted surgery : MRCAS.

[7]  André Platzer,et al.  Distributed Theorem Proving for Distributed Hybrid Systems , 2011, ICFEM.

[8]  Allison M. Okamura,et al.  Haptic Virtual Fixtures for Robot-Assisted Manipulation , 2005, ISRR.

[9]  André Platzer,et al.  Differential Dynamic Logic for Hybrid Systems , 2008, Journal of Automated Reasoning.

[10]  André Platzer,et al.  A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems , 2012, Log. Methods Comput. Sci..

[11]  André Platzer,et al.  Logical Analysis of Hybrid Systems - Proving Theorems for Complex Dynamics , 2010 .

[12]  Russell H. Taylor,et al.  Spatial Motion Constraints Using Virtual Fixtures Generated by Anatomy , 2007, IEEE Transactions on Robotics.

[13]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[14]  Peter Kazanzides,et al.  Force sensing and control for a surgical robot , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[15]  Robert D. Howe,et al.  Virtual Fixtures for Robotic Cardiac Surgery , 2001, MICCAI.

[16]  Martin Fränzle,et al.  HySAT: An efficient proof engine for bounded model checking of hybrid systems , 2007, Formal Methods Syst. Des..

[17]  Zhong Shao,et al.  Certifying the Concurrent State Table Implementation in a Surgical Robotic System ( Extended Version ) , 2011 .