A Method for Optimal Synthesis of Manipulation Robot Trajectories

Abstract

Manipulation robots belong to a class of complex, nonlinear dynamic systems. In addition, they are subjected to the constraints resulting from work-space obstacles, kinematical and physical characteristics of the mechanism itself and the actuators. Therefore, the application of optimal control theory (in energy or time optimization) leads to substantial practical difficulties, so that significant simplifications are usually performed, either in model complexity or by neglecting the existing constraints. In this paper the problem of obtaining such an optimization method, which would take into account the complete system dynamics and all the constraints is considered. The only method found to be suitable for such a complex optimization should be based on dynamic programming. In this paper an algorithm for determining optimal velocity distribution for a given manipulator tip trajectory is elaborated in detail. Practical application of the developed procedure is in off-line calculation of nominal input generalized forces (programmed control) of a nonredundant manipulator, by which the minimum of consumed energy is ensured. This is specially important for high speed motions as well as handling of heavy loads.

Optimal coordination and control of posture and movements

“…A small change of system parameters typically results in a severe degradation of performance, as compared to optimal conditions. It is therefore necessary to consider the problem of adaptation in the context of optimal control, although adaptation is a difficult topic of research [2], [6], [26], [35], [48], [97]- [100].. The adaptation included in this paper is a gradient method with a modification to Lyapunov theory similar to that reported in [78,20,51,52].…”

“…For example, considerable neural transmission time delay may place a limit upon the applicability of the feedback model. Several models of the type (1) of various biomechanical complexity have been formulated [32], [40], [97]. Elastic deformation and other structural flexibilities that can be modelled by methods of analytical mechanics may be included in the equations (1) and thus in the optimal control solution.…”

“…Already Eq. (1) covers a large model set including the equations of Hatze [32], Hemami and Farnsworth [40], Vukobratovic and Juricic [97]. Further, model extensions with various forms of friction and contact forces as well as holonomic constraints may be expressed in equations of the type (1).…”

“…The (generalised) moment of inertia M (q), the Coriolis, centripetal and frictional forces C(q,q)q, and the gravitational forces G(q) all vary along the trajectories. Several models of the type (1), varying in biomechanical complexity have been formulated hitherto: e.g., a four-segment model of Vukobratović and Juricić [97], a five-segment model of Hemami and Farnsworth [40], and a 17-segment model of Hatze [33], [32].…”

Fast Interpolation and Time-Optimization on Implicit Contact Submanifolds

“…Although trajectory optimization of free-space motions is a well-studied classical problem [7,16], less attention has been given to the setting of robots that make and break contact. The major challenge with contact is that imposes kinematic constraints that limit motion to a nonlinear submanifold in the robot's joint space.…”