Inferring Task-Space Central Pattern Generator Parameters for Closed-loop Control of Underactuated Robots

The complexity associated with the control of highly-articulated legged robots scales quickly as the number of joints increases. Traditional approaches to the control of these robots are often impractical for many real-time applications. This work thus presents a novel sampling-based planning approach for highly-articulated robots that utilizes a probabilistic graphical model (PGM) to infer in real-time how to optimally modify goal-driven, locomotive behaviors for use in closed-loop control. Locomotive behaviors are quantified in terms of the parameters associated with a network of neural oscillators, or rather a central pattern generator (CPG). For the first time, we show that the PGM can be used to optimally modulate different behaviors in real-time (i.e., to select of optimal choice of parameter values across the CPG model) in response to changes both in the local environment and in the desired control signal. The PGM is trained offline using a library of optimal behaviors that are generated using a gradient-free optimization framework.

I. Introduction

The highly-articulated nature of legged robots presents a challenge as to how to reason, in real-time, over the highdimensional spaces that underlie their various behaviors. In particular, the coordination of the limbs and their corresponding joints quickly scales in complexity. One of the most popular approaches for addressing this challenge employs randomized sampling-based planning to generate a motion plan that is subsequently executed with the help of online feedback controllers that provide regulation around the desired plan. Unfortunately, conventional techniques often do not scale efficiently as the size of the search space increases and requires the robot to comprise between optimality and reaction time. Dense sampling impedes the robot’s ability to respond to abrupt changes in the environment but allows the sampling-based motion planner to search over a diverse space of actions. Coarse sampling increases the cycle rate of the sampling-based planner at the expense of selecting from only a few (and potentially sub-optimal) actions. For the control of a highly-articulated robot, such as the hexapod in Figure 1, it is computationally prohibitive to search over all possible actions for a near-optimal solution using onboard computation. Thus, this work presents an alternative approach for closed-loop control of highly-articulated robots by encoding information about the environment, motion commands, and robot kinematics in a probabilistic graphical model (PGM) to infer parameterized motion primitives for path following control.