Prosthetic leg control in the nullspace of human interaction

Recent work has extended the control method of virtual constraints, originally developed for autonomous walking robots, to powered prosthetic legs for lower-limb amputees. Virtual constraints define desired joint patterns as functions of a mechanical phasing variable, which are typically enforced by torque control laws that linearize the output dynamics associated with the virtual constraints. However, the output dynamics of a powered prosthetic leg generally depend on the human interaction forces, which must be measured and canceled by the feedback linearizing control law. This feedback requires expensive multi-axis load cells, and actively canceling the interaction forces may minimize the human's influence over the prosthesis. To address these limitations, this paper proposes a method for projecting virtual constraints into the nullspace of the human interaction terms in the output dynamics. The projected virtual constraints naturally render the output dynamics invariant with respect to the human interaction forces, which instead enter into the internal dynamics of the partially linearized prosthetic system. This method is illustrated with simulations of a transfemoral amputee model walking with a powered knee-ankle prosthesis that is controlled via virtual constraints with and without the proposed projection.

[1]  Ludovic Righetti,et al.  Controlled Reduction With Unactuated Cyclic Variables: Application to 3D Bipedal Walking With Passive Yaw Rotation , 2013, IEEE Transactions on Automatic Control.

[2]  Koushil Sreenath,et al.  A Compliant Hybrid Zero Dynamics Controller for Stable, Efficient and Fast Bipedal Walking on MABEL , 2011, Int. J. Robotics Res..

[3]  Jonathon W. Sensinger,et al.  Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments With Transfemoral Amputees , 2014, IEEE Transactions on Robotics.

[4]  Koushil Sreenath,et al.  Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics , 2014, IEEE Transactions on Automatic Control.

[5]  Robert D. Gregg,et al.  Orthotic body-weight support through underactuated potential energy shaping with contact constraints , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[6]  Benoit Thuilot,et al.  Compass-Like Biped Robot Part I : Stability and Bifurcation of Passive Gaits , 1996 .

[7]  Jessy W. Grizzle,et al.  The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper , 2009, IEEE Transactions on Automatic Control.

[8]  Michael Goldfarb,et al.  Upslope Walking With a Powered Knee and Ankle Prosthesis: Initial Results With an Amputee Subject , 2011, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[9]  Robert D. Gregg,et al.  Hybrid invariance and stability of a feedback linearizing controller for powered prostheses , 2015, 2015 American Control Conference (ACC).

[10]  Akshay Nanjangud,et al.  SIMULTANEOUS CONTROL OF AN ANKLE-FOOT PROSTHESIS MODEL USING A VIRTUAL CONSTRAINT. , 2014, Proceedings of the ASME Dynamic Systems and Control Conference. ASME Dynamic Systems and Control Conference.

[11]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[12]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[13]  Anne E. Martin,et al.  Predicting human walking gaits with a simple planar model. , 2014, Journal of biomechanics.

[14]  Aaron D. Ames,et al.  Achieving bipedal locomotion on rough terrain through human-inspired control , 2012, 2012 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR).

[15]  Michael Goldfarb,et al.  Design and Control of a Powered Transfemoral Prosthesis , 2008, Int. J. Robotics Res..

[16]  Jessy W. Grizzle,et al.  Exponentially stabilizing continuous-time controllers for periodic orbits of hybrid systems: Application to bipedal locomotion with ground height variations , 2016, Int. J. Robotics Res..

[17]  Robert D. Gregg,et al.  Decentralized feedback controllers for exponential stabilization of hybrid periodic orbits: Application to robotic walking , 2016, 2016 American Control Conference (ACC).

[18]  Robert D. Gregg,et al.  A survey of phase variable candidates of human locomotion , 2014, 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[19]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[20]  D. Bernstein.  Matrix Mathematics: Theory, Facts, and Formulas , 2009 .

[21]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[22]  E. Westervelt,et al.  Feedback Control of Dynamic Bipedal Robot Locomotion , 2007 .

[23]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[24]  Jessy W. Grizzle,et al.  Performance Analysis and Feedback Control of ATRIAS, A Three-Dimensional Bipedal Robot , 2014 .

[25]  Kevin M. Lynch,et al.  On the Mechanics of Functional Asymmetry in Bipedal Walking , 2012, IEEE Transactions on Biomedical Engineering.

[26]  Jun Nakanishi,et al.  Operational Space Control: A Theoretical and Empirical Comparison , 2008, Int. J. Robotics Res..

[27]  Koushil Sreenath,et al.  L1 adaptive control for bipedal robots with control Lyapunov function based quadratic programs , 2015, 2015 American Control Conference (ACC).

[28]  Robert Riener,et al.  Control strategies for active lower extremity prosthetics and orthotics: a review , 2015, Journal of NeuroEngineering and Rehabilitation.

[29]  Oussama Khatib,et al.  Synthesis of Whole-Body Behaviors through Hierarchical Control of Behavioral Primitives , 2005, Int. J. Humanoid Robotics.

[30]  Jessy W. Grizzle,et al.  Continuous-time controllers for stabilizing periodic orbits of hybrid systems: Application to an underactuated 3D bipedal robot , 2014, 53rd IEEE Conference on Decision and Control.

[31]  Jonathon W. Sensinger,et al.  Experimental effective shape control of a powered transfemoral prosthesis , 2013, 2013 IEEE 13th International Conference on Rehabilitation Robotics (ICORR).

[32]  David C. Post,et al.  Design and experimental implementation of a hybrid zero dynamics-based controller for planar bipeds with curved feet , 2014, Int. J. Robotics Res..