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A deterministic optimal control problem is solved for a control-affine nonlinear system with a nonquadratic cost function. We algebraically solve the HamiltonJacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton-Jacobi partial differential equation. We interpret the value function in terms of the control Lyapunov function. Then we provide the stabilizing controller and the stability margins. Furthermore, we derive an optimal controller for a control-affine nonlinear system using the state dependent Riccati equation (SDRE) method; this method gives a similar optimal controller as the controller from the algebraic method. We also find the optimal controller when the cost function is the exponential-of-integral case, which is known as risk-sensitive (RS) control. Finally, we show that SDRE and RS methods give equivalent optimal controllers for nonlinear deterministic systems. Examples demonstrate the proposed methods.1

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This paper presents a relaxation labeling process with the newly defined compatibility measure for solving a general nonrigid point matching problem. In the literature, there exists a point matching method using relaxation labeling; however, the compatibility coefficient takes a binary value of zero or one depending on whether a point and a neighbor have corresponding points. Our approach generalizes this relaxation labeling method. The compatibility coefficient takes n-discrete values which measure the correlation between point pairs. In order to improve the speed of the algorithm, we use a diagram of log distance and polar angle bins to compute the correlation. The extensive experiments show that the proposed topology preserving relaxation algorithm significantly improves the matching performance compared to other state-of-the-art point matching algorithms.

A novel tactile imaging sensor, that is capable of measuring the elasticity of the touched object, is designed, implemented, and tested. In the proposed sensor, a multilayer Polydimethylsiloxane optical waveguide has been fabricated as the sensing probe. The light is illuminated at the critical angle to totally reflect within the flexible and transparent waveguide. When a waveguide is compressed by an object, the contact area of the waveguide deforms and causes the light to scatter. The scattered light is captured by a high-resolution camera. To find the elastic modulus of a touched object, multiple tactile images are taken from slightly different loading force values. The applied force has been estimated using the integrated pixel values of the tactile image. The strain has been estimated by matching the series of tactile images using the proposed nonrigid pattern matching algorithm. The measurement method was validated by the commercial soft polymer samples with the known elastic modulus. The experimental results showed that the tactile imaging sensor can measure the elastic modulus with the error less than 5.38%.

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