A Real-Time Energy-Optimal Trajectory Generation Method for a Servomotor System

Abstract

This paper considers real-time energy-optimal trajectory generation for a servomotor system that performs a single-axis point-to-point positioning task for a fixed time interval. The servomotor system is subject to acceleration and speed constraints. The trajectory generation is formulated as a linear-constrained optimal control problem (LCOCP), and the Pontryagin's maximum principle is applied to derive necessary optimality conditions. Instead of solving multipoint boundary value problems directly, this paper proposes a novel real-time algorithm based on two realizations: solving the LCOCP is equivalent to determining an optimal time interval of the speed-constrained arc and solving a specific acceleration-constrained optimal control problem (ACOCP), and solving an ACOCP is equivalent to determining optimal switch times of acceleration-constrained arcs and solving a specific two-point boundary value problem (TBVP). The proposed algorithm constructs sequences of time intervals, ACOCPs, switch times, and TBVPs, such that all sequences converge to their counterparts of an optimal solution of the LCOCP. Numerical simulation verifies that the proposed algorithm is capable of generating energy-optimal trajectories in real time. Experiments validate that the use of energy-optimal trajectories as references in a servomotor system does not compromise tracking performance but leads to considerable less energy consumption.

A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems

“…Wang et al [58] show an improvement of the 16% with respect to a conventional system. Richiedei et al [73] show it is possible to obtain energy savings greater than 30% of the maximum possible consumption (within the feasible domain) in a non-fixed cycle time.…”

“…However, an exception is given by the [37,84,85] works, for which an extended model of a six-degrees-of-freedom anthropomorphic industrial manipulator is created, exploiting a model-based simulation tool. Indeed, the inverse approach has been adopted on a broad variety of systems with one degree of freedom-such as a liquid-crystal display glass-handling robot [43,44,46]; a toggle mechanism [45,47]; a precision positioning table [51][52][53]; a linear axis [57]; generic, one-degree-of-freedom systems [55,56,58]; and one-degree-of-freedom manipulators mounted on a flexible base [38,39]-with two degrees of freedom with rigid [49] and flexible links [59]; with three degrees of freedom, such as a redundant planar manipulator [40,54]; and with six degrees of freedom, such as an anthropomorphic industrial manipulator [41,42,48].…”

“…Often, for serial robots, the trajectory is formulated in the joint space exploiting either a high-degree polynomial [41,[43][44][45][46][47][51][52][53] or a B-spline formulation [40,48,49]. In [42], the phase-space representation (i.e., joint velocity versus joint angle interpolation with B-splines for each joint) of the trajectory between two points is considered, while in [38,39,57] and in [55,56,58], a cycloidal trajectory and a modified parabolic velocity profile are adopted, respectively. When a high-degree polynomial formulation is chosen, the joint angular displacement is expressed as…”

“…• radial-basis function networks and genetic algorithms (RBF-GA) [38]; • Pontryagin's minimum algorithm (PMP) [55,58];…”

A Trajectory Planning-Based Energy-Optimal Method for an EMVT System

“…However, this method could not solve the optimal problem with acceleration constraint. A real-time energy-optimal trajectory generation method for a servomotor system when the system was subject to acceleration and speed constraints was proposed by Wang et al [Wang, Zhao, Bortoff et al (2015)]. The work done by Chen [Chen (2016)] used the sliding mode control and minimum-energy control to solve the optimal problem for a mechatronic motor-table system.…”