Torso height optimization for bipedal locomotion

Abstract

Bipedal robots can be better alternatives to other robots in certain applications, but their full potential can only be used if their entire kinematic range is cleverly exploited. Generating motions that are not only dynamically feasible but also take into account the kinematic limits as well as collisions in real time is one of the main challenges towards that goal. We present an approach to generate adaptable torso height trajectories to exploit the full kinematic range in bipedal locomotion. A simplified 2D model approximates the robot's full kinematic model for multiple steps ahead. It is used to optimize the torso height trajectories while taking future motion kinematics into account. The method significantly improves the robot's motion not only while walking in uneven terrain, but also during normal walking. Furthermore, we integrated the method in our framework for autonomous walking and we validated its real-time character in successfully conducted experiments.

Quintic Spline Collocation for Real-Time Biped Walking-Pattern Generation with variable Torso Height

“…Although an analytical solution to the inverse kinematics exists, cf. [6], we could not obtain an analytic expression for z t,max and z t,min respecting joint limits for ϕ A , ϕ K and ϕ H . Instead, we use a custom multi-level sampling approach 3 to find the global optima.…”

“…The BVP describing the horizontal torso motion is solved using a spline collocation method which is also the basis of our proposed algorithm. The main advantage of this method is that there is no restriction as to the shape of the ZMP or vertical torso motion, such that it can be used to incorporate kinematic constraints as shown in [6] and adapted in this paper. For the sake of brevity, we do not list methods for spline collocation here, but instead refer to [5], which collects literature related to our proposed algorithm.…”

“…We do this by finding an upper and lower limit z t,max and z t,min to which z t,des is restricted. Note that although the underlying model is almost identical to [6], we use different approaches for both, determining the limits and applying them to z t (t). Based on [21], the method presented in [6] for example assumes a fully stretched leg, i. e., ϕ K = 0, for estimating z t,max , which is not exact if we consider fixed footholds.…”

“…Note that although the underlying model is almost identical to [6], we use different approaches for both, determining the limits and applying them to z t (t). Based on [21], the method presented in [6] for example assumes a fully stretched leg, i. e., ϕ K = 0, for estimating z t,max , which is not exact if we consider fixed footholds. In contrast, we evaluate the kinematic chain of the simplified model to compute limits for the torso height given x F , z F , ϕ F , and ϕ T from Stage 1, the user-defined torso rotation ϕ t , and the provisional x t from Stage 4.…”

“…[5]. Furthermore, we avoid manually tuned parameters of the torso height optimization in [6], by following a simpler, pure geometric approach to incorporate kinematic limits. In Section II, we briefly discuss other approaches for planning feasible CoM (and whole body) motion.…”