Optimal force distribution for the legs of a walking machine with friction cone constraints

Simplified Modelling of Legs Dynamics on Quadruped Robots' Force Control Approach

“…This approach is usually applied in geometry optimisation of the mechanism design, determination of the number of joints and selection of the active joints. It's also applied in the determination of forces and torques on the active joints, and computation of force distribution among supporting legs (Klein & Kittivatcharapong, 1990;Zhang et al, 1996a;Zhang et al, 1996b). There are two methods that can be used to analyse the leg kinematic workspace: the forward analysis, and the inverse analysis.…”

“…This is quite curious to notice that ideas concerning this robotic locomotion system have been present since the first idealistic dreams of the robotics history, and nowadays this approach has gained the interest and attention of numerous researchers and laboratories. Let's mention some of the relevant works involving legged robots: Hirose et al (1989) proposes an architecture for control and supervision of walking; Klein and Kittivatcharapong (1990) study optimal distribution of the feet-soil contact forces; Vukobratovic et al (1990) work on the robot dynamics modelling and control; Pack and Kang (1995) discuss the strategies of walk control concerning the gaits; Perrin et al (1997) propose a detailed platform and legs mechanisms modelling for the dynamics simulation; Tanie (2001) discusses the new perspectives and trends for the walking machines; Schneider and Schmucker (2001) work on force control of the complete robot mechanical system.…”

Kinematic manipulability of general constrained rigid multibody systems

“…If is tall, the mechanism is over-constrained meaning some of the constraints may be removed (redundant constraints) and the constraint forces cannot be uniquely solved through rigid body formulation alone. This situation sometimes occurs in walking robots [15], [16]. If is fat the mechanism is under-constrained, meaning that the mechanism can always have internal motion even when all the active joints are locked.…”

“…Instead of the constraint (1), we replace it with a "virtual velocity" (in the same spirit as in [14] in the multiple-arm rigid grasp context): (14) Applying the principle of virtual work again, we obtain (15) where is the force that enforces the constraint (1). Since the explicit constraint is removed, we have (16) This shows that the internal force in (13) is actually the force that enforces the constraint (1).…”

“…Such systems are called hyperstatic. This problem has been noted in the walking robot literature [15], [16]. In [17], several different approaches to resolve this issue have been compared.…”