Optimal planning of an under-actuated planar body using higher-order method

Abstract

paper, an, optimal m,otion, plari,n,in,g schem,e der-actuated plan,ar gid body i s presented.A h,igh,er-order m,eth,od developed b y th,e a to con.struct th,e t7'ajectories of this system.. In this m.ethod, th,e explicit expressions for th,e states and inpu,ts in, term,s of higher derivatives of a su.bset of states i s used to ch,ange a constrainled dynamic optimization problem in,to an, mcon,, in,ed one, thereby, eliminatin,g th,e nleed for Lagranqe ~multipliers. Th,e method is applied to a two i.n,pu,t plan,ar free-floating robot with th,ree degrees-of-freedom, and th,e numerical results are repoyted.

Trajectory Planning and Control for Planar Robots with Passive Last Joint

“…Equivalently, one may say that the CP position of the last link is a flat output (Fliess et al 1995). As already mentioned, this property has already been used in various contexts, e.g., the control of a VTOL aircraft (Martin, Devasia, and Paden 1996), the trajectory planning for a planar rigid body with a single thruster (Faiz and Agrawal 1998), and within a general study of flatness in systems with a single degree of underactuation (Rathinam and Murray 1998). For the PFL system (12), the linearizing dynamic controller is obtained combining eqs.…”

“…These mechanisms arise in a number of situations, ranging from nonprehensile manipulation (Lynch and Mason 1999) to robot acrobatics (Nakanishi, Fukudu, and Koditschek 2000), from legged locomotion (Spong 1999) to surgical robotics (Funda et al 1996), from free-floating robots (Faiz and Agrawal 1998) to manipulators with flexibility concentrated at the joints (De Luca and Lucibello 1998) or distributed along the links . Another particularly interesting example is that of manipulators to be operated in spite of actuator failure (Arai and Tachi 1991).…”

“…We mention that trajectory planning results for systems that are mechanically equivalent to the latter class have been obtained based on differential flatness (Martin, Devasia, and Paden 1996;Faiz and Agrawal 1998;Rathinam and Murray 1998). On the other hand, the approach presented in De Luca and Oriolo (2000a, b), and further extended here, allows to proceed in a single framework for the gravity/no gravity case, provides a simple solution to the associated trajectory tracking problem, and explicitly addresses the issue of possible singularities affecting both planning and control, so far overlooked in other papers.…”

Task-constrained motion planning for underactuated robots

“…At this point, the tree is searched for the closest vertex to (q rand ,q rand , t rand ), according to a suitably defined metric 5 . Denote this vertex by (q near ,q near , t near ), and say it is located on a generic leaf L k .…”

“…Underactuated robots are systems that have more degrees of freedom than actuators. Underactuation arises in many situations: nonprehensile manipulation [1], acrobatic robots [2], legged locomotion [3], surgical robotics [4], free-floating robots [5] and manipulators with passive joints [6]. Other notable examples of underactuated robots are humanoids, underwater vehicles, helicopters, aircrafts and satellites.…”