Reactive Planning and Control of Planar Spring–Mass Running on Rough Terrain

Abstract

Abstract-An important motivation for work on legged robots has always been their potential for high-performance locomotion on rough terrain. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments or rely on kinematic planning at low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a planar spring-mass hopper, based on a careful characterization of the model dynamics and the design of an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a large domain of attraction that requires no explicit replanning during execution. We show in simulation that plans constructed for a simplified dynamic model can successfully control locomotion of a more complete model across rough terrain. We also characterize the performance of the planner over rough terrain and show that it is robust against both model uncertainty and measurement noise without replanning.

Parallel composition of templates for tail-energized planar hopping

“…This model is only a slight modification 7 of BHop [19]. This analytically tractable model (i) allows us to "separate" the radial dynamics (encapsulated in κ) from the contributions of the fore-aft model itself, (ii) captures the exchange of vertical and horizontal energy through stepping, and (iii) matches the empirically observed Raibert conditions (Fig.…”

“…The principal theoretical contributions are: (i) a new (slightly simplified) further abstraction ( §III-C) of the longstanding SLIP running model [3] as a formal cross-product of previously proposed vertical [18] and fore-aft [19] templates; (ii) a stability proof (modulo a restrictive assumption 3) of the parallel composition 3 of Raibert's [13] stepping controller (8) with our new energy pump (3) in Proposition 5; and (iii) a proof of local stability in the inertial reorientation model (14) of the parallel composition (15) of Raibert's [13] pitch stabilizer and the tail reorientation controller [12] in Proposition 6.…”

“…the effective coefficient of restitution through stance, or the so-called "velocity gain" during SLIP stance [19]. Note that there is a unique fixed point, κ˚" 1, in these coordinates, which is necessary and sufficient for the smooth invertibility of h κ , as can be seen by direct computation of its derivative.…”

Dynamically Consistent Online Adaptation of Fast Motions for Robotic Manipulators

“…It can be seen in Fig. 16c that the contact affects only the neighboring intervals with the disturbance torque as shown in (27).…”

“…Reactive control and robustification for the running robot are done in [27] by combining deadbeat controller and the sequential composition [28]. This method works for discrete behavioral policies and chooses goal states taken from a discrete set.…”