Control of a bow leg hopping robot

Abstract

The Bow Leg Hopper is a new type of running robot with an efficient, flexible leg. A one-legged planar prototype has been developed that passively stabilizes body attitude and is efficient enough to use on-board batteries. It is controlled by a real-time planner and has demonstrated crossing of simple artificial terrain including stepping stones and shallow stairs.The machine hops using a Bow Leg, a new type of resilient, flexible leg named for its similarity to an archery bow. The Bow Leg comprises a curved leaf spring, foot, freely pivoting hip, and the Bow String that holds the leg in compression. The Bow String is used to control the leg potential energy: it may be retracted to store energy by bending the leg, held in place, and released to perform useful work. The leg is positioned using a hobby servomotor coupled to the foot with control strings. During locomotion, the machine is controlled by actuation during flight: the leg is positioned, and the Bow String retracted to store energy that is automatically released during stance. During ground contact all the strings become slack, and the hopper bounces passively off the ground with no forces or torques supported by actuators. The hip joint is attached to the body slightly above the center of mass so the body effectively hangs from the hip during ground contact and the natural pendulum forces passively stabilize body attitude.In this design a single spring provides the leg structure, elasticity, and energy storage. The high forces of ground impact are carried conservatively by the spring and hip bearing. This addresses four problems central to dynamic legged locomotion: a low-power actuator may be used for thrust by storing energy in the leg; low-force actuation may be used to position the leg; the free hip minimizes body disturbance torques; and the hopping cycle is energy efficient since negative work is eliminated and the spring has high restitution. The machine is a form of "programmable mechanism" configured by leg position and stored energy during flight to control the evolution of the bounce dynamics.The physics of the machine have been modelled in closed form using a combination of idealized analysis and empirically determined functions. These models are used by a planner that finds sequences of foot placements across known terrain to a goal position by searching a graph representing the trajectories reachable from any given landing. The planner uses heuristics to discretize the continuous control space and estimate path costs. Paths are generated in real time as needed in conjunction with a feedback controller that rejects local disturbances.The dissertation also includes graphical methods for terrain analysis, discussion of mechanical design details, details of the real-time graph-search planner and heuristics, and experimental data from the planar prototype.

Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping

“…A number of successful robotic platforms have been built, based either directly (e.g. Raibert's runners [28], the ARL monopods [1,15], the Bow-Leg robot [37], the BiMasc platform [19] and the Jena-hopper) or indirectly (e.g. Scout quadrupeds [26], RHex [32] and Sprawl hexapods [10], BigDog [24] and others) on the principles embodied in this seemingly simple spring-mass model.…”

“…The apex return map hence takes the form (4) where several key parameters that can be used to control progression through these submaps are explicitly shown. In particular, θ td , κ c and κ d denote the familiar touchdown angle, compression and decompression spring constants as in many earlier hopper implementations [1,28], while ρ td and ρ lo denote leg lengths at touchdown and liftoff similarly to control parameters used by the Bow-Leg hopper [37]. All components of the return map, together with relevant control inputs, are illustrated in Fig.…”

“…gives independent authority over all of the apex states) [35,37], with the primary difference being in the way the energy of the system is regulated. In this paper, we will assume that the landing and liftoff leg lengths are explicitly controllable as in the Bow-Leg hopper.…”

Stride-to-stride energy regulation for robust self-stability of a torque-actuated dissipative spring-mass hopper

“…This is a principle that has been used by most successful monopod robots with a freely rotating body. 39,40 In our case, the restoring torque provided by gravity would passively counteract the leg torque, making it possible to approximately embed TD-SLIP dynamics within this more complex morphology. Further research is of course needed to establish that perturbations arising from body oscillations do not destroy TD-SLIP stability, but we think this is one of the simpler ways in which our results can be applied to physical robots.…”

Characterization of Dynamic Behaviors in a Hexapod Robot

“…Being a dimensionless quantity, specific resistance allows us to evaluate and compare a wide spectrum of systems both of biological [16] and artificial [11,15,[17][18][19][20] origin from energetic efficiency perspective. In prior work researchers successfully utilized specific resistance [4] and its variants as objective functions to empirically tune [15] behavioral controllers in legged platforms.…”