Manipulators are subject to interaction forces when they maneuver in a constrained work-space. Our goal is to develop a method for the design of controllers or constrained manipulators in the presence of model, uncertainties. The controller must carry out fine maneuvers when the manipulator is not constrained, and compliant motion, with or without Interaction-force measurement, when the manipulator is constrained. At the same time stability must be preserved If bounded uncertainties are allowed in modelling the manipulators. Stability of the manipulator and environment as a whole and the preservation of stability in the face of changes are two fundamental, issues that have been considered in the design method. We start with conventional controller design specifications concerning the treatment of external forces when the manipulator is not constrained. Generalizing this concept to include cases when the manipulator is constrained, we state a set of practical, design specifications in the frequency domain that is meaningful, from the standpoint of control, theory and assures the desired compliant motion. In the cartesian coordinate frame and stability in the presence of bounded uncertainties. This approach also assures the global stability of the manipulator and its environment. While this paper concerns the fundamentals of compliant motion, part 2 of this paper [Reference 24] is devoted to the controller design method.

A controller design methodology to develop a robust compliant motion for robot manipulators is described. The achievement of the target dynamics (the target impedance is introduced in Part I) and preservation of stability robustness in the presence of bounded model uncertainties are the key issues in the design method. State-feedback and force-feedforward gains are chosen to guarantee the achievement of the target dynamics, while preserving stability in the presence of the model uncertainties. In general, the closed-loop behavior of a system cannot be shaped arbitrarily over an arbitrarily wide frequency range. It is proved that a special class of impedances that represent our set of performance specifications are mathematically achievable asymptotically through state-feedback and interaction-force feedforward as actuator bandwidths become large, and we offer a geometrical design method for achieving them in the presence of model uncertainties. The design method reveals a classical trade-off between a system's performance over a bounded frequency range and its stability relative to model uncertainties via multivariable Nyquits criteria. Two classes of such uncertainties are dealt with. While the first class of model uncertainties is formed from the uncertainties in the parameters of the modeled dynamics, the high-frequency unmodeled dynamics form the second class of model uncertainties. The multivariable Nyquist criterion is used to examine trade-offs in stability robustness against approximation of desired target impedances over bounded frequency ranges.

A method for the design of controllers of constrained manipulators in the presence of model uncertainties is developed. The controller must carry out fine maneuvers when the manipulator is not constrained, and compliant motion, with or without interaction-force measurement, when the manipulator is constrained. At the same time stability must be preserved if bounded uncertainties are allowed in modelling the manipulators. Stability of the manipulator and environment as a whole and the preservation of stability in the face of changes are two fundamental issues that have been considered in the design method. A set of practical design specifications in the frequency domain is presented that is meaningful from the standpoint of control theory and assures the desired compliant motion in the Cartesian coordinate frame and stability in the presence of bounded uncertainties. This approach also assures the global stability of the manipulator and its environment. The consequence of inexact achievement of performance specifications on stability is also specified. Part I concerns the fundamentals of compliant motion, while Part II is devoted to the controller design method.