1,632 research outputs found

    Electrical and Computer Engineering ECE Technical Reports Purdue Libraries Year

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    Abstract This paper studies the discrete-time switched LQR (DSLQR) problem based on a dynamic programming approach. One contribution of this paper is the analytical characterization of both the value function and the optimal hybridcontrol strategy of the DSLQR problem. Their connections to the Riccati equation and the Kalman gain of the classical LQR problem are also discussed. Several interesting properties of the value functions are derived. In particular, we show that under some mild conditions, the family of finite-horizon value functions of the DSLQR problem is homogeneous (of degree 2), uniformly bounded over the unit ball, and converges exponentially fast to the infinitehorizon value function. Based on these properties, efficient algorithms are proposed to solve the finite-horizon and infinite-horizon DSLQR problems. More importantly, we establish conditions under which the strategies generated by the algorithms are stabilizing and suboptimal. These conditions are derived explicitly in terms of subsystem matrices and are thus very easy to verify. The proposed algorithms and the analysis provide a systematic way of solving the DSLQR problem with guaranteed closed-loop stability and suboptimal performance. Simulation results indicate that the proposed algorithms can efficiently solve not only specific but also randomly generated DSLQR problems, making the NP-hard problems numerically tractable

    Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

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    We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

    Model Predictive torque vectoring control for electric vehicles near the limits of handling

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    In this paper we propose a constrained optimal control architecture to stabilize a vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear vehicle and tyre model is employed to find reference steady-state cornering conditions as well as to design a linear Model Predictive Control (MPC) strategy using the rear wheels' slip ratios as input. A Sliding Mode Slip Controller then calculates the necessary motor torques according to the requested wheel slip ratios. After analysing the relative trade-offs between performance and computational effort for the MPC strategy, we validate the controller and compare it against a simpler unconstrained optimal control strategy in a high fidelity simulation environment

    Consistent Approximations for the Optimal Control of Constrained Switched Systems

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    Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In this paper, we devise an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time. Our approach, which we prove converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, then performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical Chattering Lemma that we prove. We extend this algorithm by formulating a computationally implementable algorithm which works by discretizing the time interval over which the switched dynamical system is defined. Importantly, we prove that this implementable algorithm constructs a sequence of points by recursive application that converge to the local minimizers of the original constrained optimal control problem. Four simulation experiments are included to validate the theoretical developments
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