Time optimal trajectory planning for robotic manipulators with obstacle avoidance: A CAD approach

Abstract

A method is p r e s e n t e d w h i c h f i n d s t h e minirnum time motions f o r a manipulator between given end s t a t e s . Tne method c o n s i d e r s t h e f u l l n o n l i n e a r m a n i p u l a t o r d y n a m i c s , a c t u a t o r s a t u r a t i o n c h a r a c t e r i s t i c s , and a c c o u n t s f o r b o t h t h e p r e s e n c e o f o o s t a c l e s i n t h e work spaca and r e s t r i c t i o n s on the motions of the m a n i p u l a t o r ' s j o i n t s . . It c o n s i d e r s t h e f u l l nonlinear dynamics of the manipulator and permits a c t u a t o r c o n s t r a i n t s t o b e e x p r e s s e d as complex f u n c t i o n s o f t h e s y s t e m s t a t e . S u b s e q u e n t r e s e a c h h a s shown t n e a l g o r t i h m is p r a c t i c a l f o r c o n t r o l l i n g g e n e r a l s i x d e g r e e -o f -f r e e d o m m a n i p u l a t o r s , a u s e f u l d e s i g n t o o l when used i n t h e form of a h i g h l y i n t e r a c t i v e program, and t h a t i t can be e x t e n d e d t o i n c l u d e s u c h c o n s t r a i n t s as t h e maximum d y n a m i c f o r c e s t h a t a n o b j e c t b e i n g t o l e r a t e a n d t h e s p e e d s which a rnanipulato s u s t a i n w i t h o u t l o s i n g its g r a s p o f t h e o b j e c t S u b s e q u e n t l y , o t h e r r z s e a r c h ~f s have suggested e s s e n t i a l l y t h e same a l g o r i t h m . ; : : : ? : 8 $ , i y R e c e n t r e s e a r c h s u g g e s t s t h a t l $ h i s a l g o r i t h m may be used to find optirnal paths . Conceptually t h e a l g o r i t n m c o u l d s e a r c h v a r i o u s p a t h s f o r t h e one with the lowest time.

Minimum-time speed optimisation over a fixed path

“…Once the path is reparameterised in this manner, using the vehicle dynamics, valid velocity regions are determined. The goal then becomes to find valid velocity profiles along the newly parameterised paths that stay below the maximumvelocity regions (Bobrow et al, 1985;Constantinescu & Croft, 2000;Dubowsky, Norris, & Shiller, 1986;Pfeiffer & Johanni, 1987;Shin & McKay, 1985). Another approach to the more general trajectory problem was to modify this method to allow modest changes to the trajectory (Bayer & Hauser, 2012;Shiller, 1994;Shiller & Dubowsky, 1989), but we will not be exploring those extensions.…”

Combining discrete and continuous optimization to solve kinodynamic motion planning problems

“…This expression was first introduced by Donald et al (1993). However, finding the optimal collision-free trajectory is an old and still topical subject in robotics, which received several names: minimum time path planning Johnson and Gilbert 1985), optimal robot path planning using the minimum-time criterion (Bobrow 1988), trajectory planning or modeling (Dubowsky et al 1989;Saramago and Steffen 2001).…”

“…There exist several approaches to solve this optimal control problem. The first approach was introduced by Gilbert and Johnson in Johnson and Gilbert (1985) and extended by other authors, such as Bobrow (1988) and Dubowsky et al (1989). The technique first discretizes the state variable with B-splines and then looks for a control variable that satisfies the dynamic constraints and minimizes the travel time.…”

Interactive time optimal robot motion planning and work-cell layout design

“…Several numerical methods for obtaining time optimal robot motions have been developed, using the Pontryagin Maximum Principle [1,2], a search in the state space [4], and parameter optimizations [4,6], most of which have been demonstrated for very simple two and three link manipulators [I- 3,6]. The presence of obstacles, makes the path planning problem even harder, increasing computation with the number and complexity of the obstacles [4, 6,9,10].…”