A new linear optimal guidance law for impact angle interception ispresented. The linearization of the non-linear equations of motion isperformed around a nominal circular trajectory, thus allowing the linearizationto be valid far from the initial line-of-sight. The proposed lawcan be viewed as a generalization of the optimal rendezvous problem.Closed form expressions for the miss distance, the intercept angle error,and the control effort are derived for the linear model. The transformationfrom the relative position and the relative velocity, with respect tothe circular trajectory, to the relative inscribed angle and the relative inscribedangle rate is presented. Using this transformation, the implementationof the optimal impact angle guidance law based on the inscribedangle is derived. The application in various scenarios enforcing differentimpact angles is studied via nonlinear simulations, and it is shownthat for the investigated parameters the proposed law performs betterwhen compared to biased proportional navigation guidance. The nonlinearsimulations also show that for investigated parameters, although theoptimality is guaranteed only around the nominal circular trajectory, theproposed guidance law enables to impose the desired impact angles evenwhen the deviations from the nominal trajectory are not small.
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