Isaac Klickstein

Isaac Klickstein

Engineering PhD applying numerical methods to solve controls and optimization problems

Optimal Control Problem: Double Integrator Obstacle Avoidance

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Obstacle Avoidance for Double Integrators

\[\begin{aligned} \min && &J = \frac{1}{2} \int_0^{t_f} \left( u_x^2(t) + u_y^2(t) \right) dt\\ \text{s.t.} && &\dot{x}(t) = v(t), \quad x(0) = x_0, \quad x(t_f) = x_f\\ && &\dot{v}(t) = u_x(t), \quad v(0) = v_0, \quad v(t_f) = v_f\\ && &\dot{y}(t) = w(t), \quad y(0) = y_0, \quad y(t_f) = y_f\\ && &\dot{w}(t) = u_y(t), \quad w(0) = w_0, \quad w(t_f) = w_f\\ && &(x(t) - c_x)^2 + (y(t) - c_y)^2 \geq r^2 \end{aligned}\]

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