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weiwei_ilqg_biological - Submitted to the 1st International...

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Submitted to the 1 st International Conference on Informatics in Control, Automation and Robotics 1 Iterative Linear Quadratic Regulator Design for Nonlinear Biological Movement Systems Weiwei Li Department of Mechanical and Aerospace Engineering University of California San Diego La Jolla, CA 92093-0411 [email protected] Emanuel Todorov Department of Cognitive Science University of California San Diego La Jolla, CA 92093-0515 [email protected] Abstract This paper presents an Iterative Linear Quadratic Reg- ulator (ILQR) method for locally-optimal feedback control of nonlinear dynamical systems. The method is applied to a musculo-skeletal arm model with 10 state dimensions and 6 controls, and is used to com- pute energy-optimal reaching movements. Numerical comparisons with three existing methods demonstrate that the new method converges substantially faster and finds slightly better solutions. Keywords : ILQR, Optimal control, Nonlinear system 1 Introduction Optimal control theory has received a great deal of at- tention since the late 1950s, and has found applica- tions in many fields of science and engineering. It has also provided the most fruitful general framework for constructing models of biological movement[3, 8, 11]. In the field of motor control, optimality principles not only yield accurate descriptions of observed phenom- ena, but are well justified a priori . This is because the sensorimotor system is the product of optimization processes (i.e. evolution, development, learning, adap- tation) which continuously improve behavioral perfor- mance. Producing even the simplest movement involves an enormous amount of information processing. When we move our hand to a target, there are infinitely many possible paths and velocity profiles that the multi-joint arm could take, and furthermore each trajectory can be generated by an infinite variety of muscle activa- tion patterns (since we have many more muscles than joints). Biomechanical redundancy makes the motor system very flexible, but at the same time requires a very well designed controller that can choose intelli- gently among the many possible alternatives. Optimal control theory provides a principled approach to this problem – it postulates that the movement patterns being chosen are the ones optimal for the task at hand. The majority of existing optimality models in motor control have been formulated in open-loop. However, the most remarkable property of biological movements (in comparison with synthetic ones) is that they can accomplish complex high-level goals in the presence of large internal fluctuations, noise, delays, and unpre- dictable changes in the environment. This is only pos- sible through an elaborate feedback control scheme. In- deed, focus has recently shifted towards stochastic op- timal feedback control models. This approach has al- ready clarified a number of long-standing issues related to the control of redundant biomechanical systems[8].
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