In this paper, we consider the problem of evaluating plan fragments for insertion into an existing plan. Preparing a plan that is robust to variations in continuous resources requires considering the uncertainty over these resources. For some situations, it is impractical to add branches to the plan a priori, because such situations may arise at any of a large number of points in execution. Adding all these potential branches to an existing plan would require an immense computational effort and result in a huge plan. In such a case, it makes more sense to precompute a plan fragment to react to such a situation and allow the execution system to insert the plan fragment into its current plan when appropriate. The problem can thus be seen as a restricted form of plan merging, but with the addition of uncertainty and continuous resources, and the criterion of maximizing utility rather than absolute goal achievement. We formalize the problem and introduce an efficient solution method, incremental bounds refinement, that iteratively narrows bounds on the expected value of adding a branch until it can be discriminated from the original plan.

Binary actuators have only two discrete states (denoted '0' and '1'), both of which are stable without feedback. As a result, manipulators built with binary actuators have a finite number of states. Compared to a manipulator built with continuous actuators, a binary manipulator provides good performance, and is also relatively inexpensive. However, the number of states of a binary manipulator grows exponentially with the number of actuators. While this makes the calculation of its inverse kinematics quite difficult, the discrete nature of a binary manipulator makes it possible to compute its forward kinematics more efficiently than for a continuously actuated manipulator. By pre-computing all possible configurations of each module of a binary manipulator (a finite and usually small number) it is possible to compute the forward kinematics from a set of joint parameters without using any transcendental functions.

Binary manipulators are powered by actuators which have only two stable states. Therefore, they can reach only a discrete (but possibly large) number of locations. Compared to a manipulator built with continuous actuators, a binary manipulator provides reasonable performance, and is relatively inexpensive (up to an order of magnitude cheaper). The number of states of a binary manipulator grows exponentially with the number of actuators. This makes the calculation of its inverse kinematics quite difficult. This paper presents a combinatorial method for computing the inverse kinematics of a binary manipulator that reduces the search space to a manageable size. It also creates reasonably smooth motions that follow a specified trajectory accurately (in both position and orientation), despite the discrete nature of binary actuation.

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators built with binary actuators have a finite number of states. The major benefits of binary actuation are that extensive feedback control is not required, task repeatability can be very high, and two-state actuators are generally very inexpensive, resulting in low cost robotic mechanisms. These manipulators therefore have great potential for use in the service sector, where the cost of standard, high performance, robotic manipulators is often difficult to justify. A binary manipulator by contrast, provides good performance, and is also relatively inexpensive. The most difficult challenge with a binary manipulator is to control it efficiently. Given that the number of configurations attainable by binary manipulators grows expotentially in the number of actuated degrees of freedom, calculation of inverse kinematics by direct enumeration of joint states and calculation of forward kinematics is not feasible in the highly actuated case. This paper presents an efficient method for performing binary manipulator inverse kinematics based on a continuum approach.