Constrained receding horizon controllers are often designed to regulate the system state about some desired set-point subject to input constraints. This paper presents a class of receding horizon controllers which force the inputs to lie inside the constraint set by including a so-called `recentred barrier function'. The significance of such a controller is that hard constraints are replaced with penalty type soft constraints. This results in a control law that `backs off' near constraint boundaries. The degree to which this backing-off occurs, is directly related to the parameter value that characterises the class of controllers. For each parameter value there is a corresponding unconstrained minimisation problem. The associated control law is obtained in the standard manner by solving this problem at each time interval and applying the first control move to the system. This method is applicable to general convex objective functions with convex inequality constraints. We illustrate this idea by way of an example application to linear discrete-time plant models with linear and convex quadratic static input constraints.