We present a new method to reconstruct the shape of an unknown object using tactile sensors, without requiring object immobilization. Instead, sensing and nonprehensile manipulation occur simultaneously. The robot infers the shape, motion and center of mass of the object based on the motion of the contact points as measured by the tactile sensors. This allows for a natural, continuous interaction between manipulation and sensing. We analyze the planar case first by assuming quasistatic dynamics, and present simulation results and experimental results obtained using this analysis. We extend this analysis to the full dynamics and prove observability of the nonlinear system describing the shape and motion of the object being manipulated. In our simulations, a simple observer based on Newton's method for root finding can recover unknown shapes with almost negligible errors. Using the same framework we can also describe the shape and dynamics of three-dimensional objects. However, there are some fundamental differences between the planar and three-dimensional case, due to increased tangent dimensionality. Also, perfect global shape reconstruction is impossible in the 3D case, but it is almost trivial to obtain upper and lower bounds on the shape. The 3D shape reconstruction method has also been implemented and we present some simulation results.

126 pages

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