Review and descriptive investigation of the connection between bipedal locomotion and non-prehensile manipulation

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…to the hopper, and vice-versa as alluded to above, this analogy is extended in [70] to bipedal locomotion and juggling systems, with a common control strategy). More complex jumping robots with 6 DoF and nonlinear dynamics can be recast directly into (1), see [184,Equations ( 4)- (10)].…”

“…Another aerocrane configuration is with a controlled payload, while the airship floats in the air [240,241]. Then the roles of the robot and the object are reversed compared to (70). It is also possible to add complementarity constraints of the form 0 ≤ λ n,2 ⊥ x 1 − l ≥ 0, which models the ground inpenetrability [242], or more to model possible obstacles that the payload may collide with.…”

“…Different approaches are proposed in [114,285], which instead use impacts to improve the observability, and in [286] where a dead-beat discrete-time observer is designed for the time-discretized complementarity dynamics (the time-discretization is obtained with an event-capturing time-stepping scheme [7]). In [70] a finite-time state observer is included in the closed-loop design, and applied to a 2-DoF juggler (made of two tapping robots as in Fig. 3 (b)).…”

“…The principle is to track the object's motion and to design a mirror-like motion of the object's motion for the robot, and regulating the object at impacts. Similarly to the OGY method, this seems to mainly apply to juggling systems which satisfy M 2 (q) ≫ M 1 (q) (hence q2 remains continuous at impacts, an assumption that is widely spread in juggling systems analysis [334,159,257,59,158,216,141,335,70,275,327,140]). The dead-beat controller designed in [13,14] is shown to reduce to a mirror algorithm when this assumption holds.…”

“…The main objective of this article is to show that several classes of robotic systems and tasks can be recast into the general framework of (1), a work initiated in [1,3,15] [2, sections 8.7, 8.8, 8.9], more recently in [70] where bipedal locomotion and non-prehensile manipulation are studied from a common point of view (hence [70] extends, in a sense, [15]), in [31] where the analogy between balancing a biped and grasping an object is used. This article is organised as follows: the contact problem and the impact dynamics are introduced in section 2; section 3 presents several typical examples of robot-object systems, as well as extensions and new applications; section 4 is dedicated to survey the various analytical tools which have been used to study the control of subclasses of (1); section 5 reviews important modeling features; section 6 surveys the existing control strategies; section 7 is devoted to discrete-time issues.…”