Online time-optimal trajectory planning in dynamic workspace of cable suspended robots

Abstract

This paper presents a method for online trajectory planning of cable suspended robots. A three degrees-of-freedom spatial cable robot is studied in this analysis. By deriving dynamic model of the robot, cable force restrictions will induce a set of algebraic inequalities in dynamic equations. Direction of required tracking acceleration reveals feasible motion of the robot, which guarantees non-violation of cable force bilateral bounds. Required tracking acceleration is in the direction of instantaneous minus desired velocity vectors with specified magnitude. Furthermore, alternative recipes are employed to decrease negative impacts of unwanted inputs and applying actuator constraints in trajectory planning. Finally, several simulations are presented to demonstrate success of the method. Proposed approach can be used in online trajectory tracking for all cabledriven parallel suspended robots akin to what is realized for the presented three degrees-of-freedom robot.

Randomized Kinodynamic Planning for Cable-Suspended Parallel Robots

“…Then, X becomes a nonlinear manifold of dimension d X = 2(n q − n e ) generically, defined implicitly by Eqs. 1and (2). Irrespective of the form of X , the motions must always be confined to a feasibility region X feas ⊆ X of collision-free states respecting joint and constraint force limits (such as tension positivities in cable-driven robots).…”

“…This fact complicates the generation of RRTs over X , because there is no straightforward way to randomly select points x x x = (q q q,q q q) satisfying Eqs. (1) and (2), and the numerical integration of Eq. (3) easily drifts away from X when standard methods for ordinary differential equations are used.…”

“…For instance, in [11] cyclic trajectories leaving the static workspace were given, and the approach was later extended to synthesize point-to-point trajectories for pick-and-place tasks [10,14]. Optimal control methods for Robocrane-type platforms were also provided in [2]. While such methods are remarkable, none of them were designed to avoid collisions.…”