Browsing by Author "Awasthi, Chaitanya"

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    Computational Multi-material Inverse Design of Soft Robotic Actuators via Nonlinear Functional Optimization
    (2023-08) Awasthi, Chaitanya
    The compliant nature of soft robotic actuators allows them to maneuver and interact with the environment in ways which are more adaptable and inherently safer compared to the traditional rigid body robots. However, this compliance makes it difficult to control their deformation as these actuators can potentially have infinite degrees of freedom. Controlling the deformation of a soft robotic actuator has potential applications in fields requiring precise control over the shape of the robot. Areas such as medical robotics can use the shape control of soft robots to gently treat aneurysms in humans or deliver medicines within the body, among other applications. However, given a known external loading, it is usually not possible to deform a soft robot into an arbitrary shape if it is fabricated using only a single material. Even if the robot is fabricated using multiple materials, there is a lack of "voxel-level" material tuning to allow for the generation of a soft robot that can take an arbitrary shape. A major contribution of this dissertation is the proposal of a new physics-based method for the computational design of soft hyperelastic robotic actuators to address this problem. The method takes as input an undeformed robot shape, a specified external load, and a user desired final shape. It then solves an inverse problem in design using nonlinear optimization subject to physics constraints. The nonlinear program is solved using a gradient-based interior-point method. Analytical gradients are computed for efficiency. The method outputs fields of material properties, at the level of individual voxels, which can be used to fabricate a soft robot. A body fabricated to match this material field is expected to deform into a user-desired shape, given the same external loading input. The inverse design method is tested for validity and robustness. The performance of the method is tested on several example cases in silico. Another key contribution of the present work is the development of an adaptive impedance controller that allows for a rigid robot (a single degree of freedom indenter) to safely interact with an unknown soft environment, such as a body tissue. The controller is mathematically proven to be asymptotically stable and the simulation results demonstrate the efficacy of the controller in achieving force tracking without the use of a force sensor. The results show that this force tracking is achieved through the asymptotic convergence of the estimated tissue parameters to the true tissue parameters.
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    Forward and Inverse Methods in Optimal Control and Dynamic Game Theory
    (2019-08) Awasthi, Chaitanya
    Optimal control theory is ubiquitous in mathematical sciences and engineering. However, in a classroom setting we barely move beyond linear quadratic regulator problems, if at all. In this work, we demystify the necessary conditions of optimality associated with nonlinear optimal control by deriving them from first principles. We also present two numerical schemes for solving these problems. Moving forward, we present an extension of inverse optimal control, which is the problem of computing a cost function with respect to which observed state and control trajectories are optimal. This extension helps us to handle systems which are subjected to state and/or control constraints. We then generalize the methodology of optimal control theory to solve constrained non-zero sum dynamic games. Dynamic games are optimization problems involving several players who are trying to optimize their respective cost functions subject to constraints. We present a novel method to compute Nash equilibrium associated with a game by combining aspects from direct and indirect methods of solving optimal control problems. Finally, we study constrained inverse dynamic games, which is a problem analogous to constrained inverse optimal control method. Here, we show that an inverse dynamic game problem can be decoupled and solved as an inverse optimal control problem for each of the players individually. Throughout the work, examples are provided to demonstrate efficacy of the methods developed.