In the past decade, research advances in robot dynamic simulation have included algorithms for space robots operating as open chain mechanisms and earth-bound robot systems operating under constrained motion conditions. Few researchers, however, have investigated a combination of these conditions, i.e. a space robot performing closed chain operations. This paper presents a generalized formulation of the dynamic equations for a space-based robot in both open chain and closed chain configurations. This formulation represents the consolidation of several specialized formulations into a single convenient form.

The operational space inertia matrix Lambda reflects the dynamic properties of a robot manipulator to its tip. In the control domain, it may be used to decouple force and/or motion control about the manipulator workspace axes. The matrix Lambda also plays an important role in the development of efficient algorithms for the dynamic simulation of closed-chain robotic mechanisms, such as multiple manipulator systems and walking machines. This paper presents the development of a recursive algorithm for computing the operational space inertia matrix (OSIM) that reduces the computational complexity to O(N). This algorithm, the inertia propagation method, is based on a single recursion that begins at the base of the manipulator and progresses out to the last link. Also applicable to redundant systems and mechanisms with multiple-degree-of-freedom joints, the inertia propagation method is the most efficient method known for computing Lambda for N>or=6. The numerical accuracy of the algorithm is discussed for a PUMA 560 robot with a fixed base.>

An efficient serial algorithm for the dynamic simulation of a single closed chain is developed. The algorithm is valid for a manipulator with any number of degrees of freedom, N, and it is still applicable when the manipulator is in a singular position. A moving base may also be incorporated into the system. Arbitrary joints are allowed, including multiple-degree-of-freedom joints, and a general contact model is used. The operational space inertia matrix of the chain is used to solve for the unknown contact force vector at the tip, which is then used in the solution for the closed chain joint accelerations. The final solution requires only an additional n/sub c/*n/sub c/ matrix inverse for the closed chain part, where n/sub c/ is the number of degrees of constraint at the manipulator tip. The computational complexity of the algorithm is (ON/sup 3/). The reduction of the order of computation complexity of O(N) is briefly discussed.>

The development of a recursive algorithm for the operational space inertia matrix, the inertia propagation method, which reduces the computational complexity to O(N) for any manipulator is presented. The algorithm is based on a single recursion which begins at the base of the manipulator and progresses out to the last link. Spatial articulated transformations are utilized in the recursion procedure. The algorithm is the most efficient method known for N>or=6. The numerical accuracy of the algorithm is tested for a PUMA 560 robot with a fixed base. The results demonstrate the accuracy of the inertia propagation method for such a configuration.>