A Variational Approach To The Optimization of Gait For a Bipedal Robot

Abstract

This paper presents a method for optimizing the walking motions of a planar five-link biped. The technique starts with non-linear kinematic and dynamic models for both the single-support and impact stages of motion. A variational technique is then used to derive joint trajectories that minimize a simple cost function. The resulting two-point boundary value problem is solved using a finite difference technique, with trajectories obtained from a simple linearized model as initial conditions. Families of optimal trajectories for different step periods and step lengths are presented.

Fast Interpolation and Time-Optimization on Implicit Contact Submanifolds

“…A common trajectory optimization approach for legged robots is to formulate a large nonlinear optimization problem over both joint trajectories and timing [3,6,8,11,12]. Because of their computational expense, these methods appear best suited for generating gait cycles [3,11,12] or offline primitives to be reused later [6,8].…”

“…Because of their computational expense, these methods appear best suited for generating gait cycles [3,11,12] or offline primitives to be reused later [6,8]. Full trajectory optimization poses other challenges as well.…”

“…Another problem is maintaining loop closure constraints at contacts. Some authors parameterize the manifold of closed-loop configurations at each possible contact state [3,6,8], while others enforce loop closure implicitly by adding nonlinear equality constraints at collocation points along the trajectory [11]. Parameterization is manageable for a small number of contact states (e.g., left foot, right foot, and two foot support) but is challenging and tedious when hands, knees, and elbows may be involved in contact.…”

“…The major challenge with contact is that imposes kinematic constraints that limit motion to a nonlinear submanifold in the robot's joint space. Prior work on optimizing robot locomotion and manipulation trajectories [3,6,8,11,12] relies on descent-based approaches that are often extremely slow, taking minutes or hours to complete, and require careful choice of initial trajectories to avoid falling into local minima. As a result, these methods are best suited for offline trajectory generation.…”

Development of a CORBA-based Humanoid Robot and its Applications

“…In (Silva et al, 1999), the body link is restricted to the vertical position, the body forward velocity is considered to be constant and the tip motion of the swing leg is constrained to follow sinusoidal functions. The effect of the walking velocity and step length on the consumed energy is treated in (Channon et al, 1996). A variation technique is used to minimize the cost function.…”