This paper extends a previous method aimed to compute discrete time-optimal trajectories of “dot-like” robots to consider the general case of robotic manipulators. The resulting trajectories provide the torque command at each actuator for following a given path in minimum time while respecting the constraints imposed by the manipulator model.
The proposed method makes use of a modified manipulator dynamic model in terms of γ, the arc length parameter which defines the trajectory in the joint space q. The search for a solution is done in the space specified by γ and its derivative ν (the pseudo-speed scalar). In this space we define the features of the solution in order to design an efficient algorithm to compute the time-optimal trajectory. We determine bounds to the model components, such that the optimal solution lies below a curve limiting the area Ω, area in which all possible solutions fit.
The algorithm performs, inside Ω, an ascendent search of the limiting curve; this strategy permits the curve obtained at each intermediate step to be a valid solution.