Estimation of crank angle for cycling with a powered prosthesis

In order for a prosthesis to restore power generation during cycling, it must supply torque in a manner that is coordinated with the motion of the bicycle crank. This paper outlines an algorithm for the real time estimation of the angular position of a bicycle crankshaft using only measurements internal to an intelligent knee and ankle prosthesis. The algorithm assumes that the rider/prosthesis/bicycle system can be modeled as a four-bar mechanism. Assuming that a prosthesis can generate two independent angular measurements of the mechanism (in this case the knee angle and the absolute orientation of the shank), Freudenstein's equation can be used to synthesize the mechanism continuously. A recursive least-squares algorithm is implemented to estimate the Freudenstein coefficients, and the resulting link lengths are used to reformulate the equation in terms of input-output relationships mapping both measured angles to the crank angle. Using two independent measurements allows the algorithm to uniquely determine the crank angle from multi-valued functions. In order to validate the algorithm, a bicycle was mounted on a trainer and configured with the prosthesis using an artificial hip joint attached to the seat post. Motion capture was used to monitor the mechanism for forward and backward pedaling and the results are compared to the output of the presented algorithm. Once the parameters have converged, the algorithm is shown to predict the crank angle within 15° of the externally measured value throughout the entire crank cycle during forward rotation.