We presented our constraint-based programming approach, iTaSC, that formulates instantaneous sensor-based robot tasks as constraint sets, and subsequently solves a corresponding least-squares problem to obtain control set points, such as desired joint velocities or joint torques. This paper further extends this approach, (i) by explicitly supporting the inclusion of inequality constraints in the task and (ii) by supporting a broader class of objective functions for translating the task constraints into robot motion. These extensions are made while retaining a tractable mathematical problem structure (a convex program). Furthermore, first results on extending the approach to non-instantaneous tasks are presented. As illustrated in the paper, the power of the approach lies (i) at its versatility to specify a wide range of robot behaviors and the ease of making task adjustments, and (ii) at its generic nature, that permits using systematic procedures to derive the underlying control equations.