In a recent work, we have introduced a new multiple constant multiplication (MCM) algorithm, denoted as RADIX-2 r. The latter exhibits the best results in speed and power, comparatively with the most prominent algorithms. In this paper, the area aspect of RADIX-2 r is more specially investigated. RADIX-2 r is confronted to area efficient algorithms, notably to the cumulative benefit heuristic (Hcub) known for its lowest adder-cost. A number of benchmark FIR filters of growing complexity served for comparison. The results showed that RADIX-2 r is better than Hcub in area, especially for high order filters where the saving ranges from 1.50% up to 3.46%. This advantage is analytically proved and experimentally confirmed using a 65nm CMOS technology. Area efficiency is achieved along with important savings in speed and power, ranging from 6.37% up to 38.01% and from 9.30% up to 25.85%, respectively. When MCM blocks are implemented alone, the savings are higher: 10.18%, 47.24%, and 41.27% in area, speed, and power, respectively. Most importantly, we prove that MCM heuristics using similar addition pattern (A-operation with the same shift spans) as Hcub yield excessive bit-adder overhead in MCM problems of high complexity. As such, they are not competitive to RADIX-2 r in high order filters.

Force/position control strategies provide an effective framework to deal with tasks involving interaction with the environment. One of these strategies proposed in the literature is external force feedback loop control. It fully employs the available sensor measurements by operating the control action in a full dimensional space without using selection matrices. The performance of this control strategy is affected by uncertainties in both the robot dynamic model and environment stiffness. The purpose of this paper is to improve controller robustness by applying a neural network technique in order to compensate the effect of uncertainties in the robot model. We show that this control strategy is robust with respect to payload uncertainties, position and environment stiffness, and dry and viscous friction. Simulation results for a three degrees-of-freedom manipulator and various types of environments and trajectories show the effectiveness of the suggested approach compared with classical external force feedback loop structures.

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