Is the way that we interpret the coefficients of a robust linear regression (rlm function in R) is the same as the OLS regression? Can I interpret the coefficient of a robust regression (forexample) in the following way:
Suppose that Age is a predictor and Systolic is a dependent variable, so we can say that with every increase of one year in age, the systolic BP (on the average) increases by 1.051 (95% CI 0.752 to 1.350) units
In robust linear regression, the model you are estimating is still a linear regression, and the coefficients of the predictor variables in the model still has the same interpretation, they are simply partial derivatives. So the answer is, YES, the interpretation is the same.
For more detailed answers to a similar question, see Interpret regression coefficients after WLS