Optimal Trajectory Generation for Manipulator Robots under Thermal Constraints

Abstract

We propose here to deal with the optimization of velocity profiles of manipulator robots with a minimum time criterion subject to thermal constraints. This paper deals with the real impact of thermal limitations on optimal velocity profiles and the methods to calculate the corresponding optimal trajectories. We first calculate analytically the optimal solution in a simple case in order to verify the validity of the numerical algorithm and also to present a general methodology to calculate optimal trajectories in robotics using results from the theory of calculus of variations and not from the theory of optimal control. We derive then a numerical algorithm based on the discretization of the time law through an interpolation with non uniform cubic splines. This algorithm shows robust and efficient convergence properties and the trajectories thus generated were executed successfully on a Stäubli Rx90.

Time-Optimal Path Tracking for Robots: A Convex Optimization Approach

“…Other approaches to limit the rate of change of the torques consist of directly imposing upper and lower bounds on this rate of change [17], [23], or choosing a parameterization for the pseudo-accelerations that is at least piecewise continuous [23]. Another important motivation for choosing γ 1 > 0, on the other hand, is to limit the thermal energy dissipated by the actuators, so as to prevent actuator overheating if the task is carried out repeatedly [38].…”

Time-energy optimal path tracking for robots: a numerically efficient optimization approach

“…Using equation (25) to calculate the integral in equation (26) analytically, the right-hand side of equation (26) can be rewritten as…”

“…Two important motivations for having a nonzero γ > 0 is to limit the rate of change of the torques [14], such that the actuators can better handle the torque demand and to limit the thermal energy dissipated by the actuators, so as to prevent actuator overheating if the task is carried out repeatedly [25]. T 0 (τ i (t) 2 /τ 2 i )dt if γ is varied between 0 and 10 0.6 .…”

Optimal trajectory generation with DMOC versus NTG : application to an underwater glider and a JPL aerobot.

“…To solve optimal control problems numerically, the paper [24] proposed that control states can be approximated by values at a finite number of time points, the control history can be parametrized by piecewise polynomials, and further this problem can be solved by a standard Non- Optimal trajectory generation problem is one kind of optimal control problems. Its applications vary from the control of various devices such as control of linear system [25], and engine valves [26], to motion planning of robots [27] [28], manipulator robots [29] [3~], humanoid robot [31], and trajectory tracking for boom cranes [32]. Optimal trajectory generation for hypersonic vehicles as a research topic was raised in [33], Philip D. Hattis and Richard K. Smolskis proposed a calculus of variations direct method of steepest descent to determine the trajectory for hypersonic vehicles.…”