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Register a new userEvolution of central pattern generators for the control of a five-link bipedal walking mechanism
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Atilim Gunes Baydin
Publication date
2012
fields
Informatics Engineering
and research's language is
English
Authors
Atilim Gunes Baydin
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Central pattern generators (CPGs), with a basis is neurophysiological studies, are a type of neural network for the generation of rhythmic motion. While CPGs are being increasingly used in robot control, most applications are hand-tuned for a specific task and it is acknowledged in the field that generic methods and design principles for creating individual networks for a given task are lacking. This study presents an approach where the connectivity and oscillatory parameters of a CPG network are determined by an evolutionary algorithm with fitness evaluations in a realistic simulation with accurate physics. We apply this technique to a five-link planar walking mechanism to demonstrate its feasibility and performance. In addition, to see whether results from simulation can be acceptably transferred to real robot hardware, the best evolved CPG network is also tested on a real mechanism. Our results also confirm that the biologically inspired CPG model is well suited for legged locomotion, since a diverse manifestation of networks have been observed to succeed in fitness simulations during evolution.
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The complexity of bipedal locomotion may be attributed to the difficulty in synchronizing joint movements while at the same time achieving high-level objectives such as walking in a particular direction. Artificial central pattern generators (CPGs) can produce synchronized joint movements and have been used in the past for bipedal locomotion. However, most existing CPG-based approaches do not address the problem of high-level control explicitly. We propose a novel hierarchical control mechanism for bipedal locomotion where an optimized CPG network is used for joint control and a neural network acts as a high-level controller for modulating the CPG network. By separating motion generation from motion modulation, the high-level controller does not need to control individual joints directly but instead can develop to achieve a higher goal using a low-dimensional control signal. The feasibility of the hierarchical controller is demonstrated through simulation experiments using the Neuro-Inspired Companion (NICO) robot. Experimental results demonstrate the controllers ability to function even without the availability of an exact robot model.
Central Pattern Generators (CPGs) have several properties desirable for locomotion: they generate smooth trajectories, are robust to perturbations and are simple to implement. Although conceptually promising, we argue that the full potential of CPGs has so far been limited by insufficient sensory-feedback information. This paper proposes a new methodology that allows tuning CPG controllers through gradient-based optimization in a Reinforcement Learning (RL) setting. To the best of our knowledge, this is the first time CPGs have been trained in conjunction with a MultilayerPerceptron (MLP) network in a Deep-RL context. In particular, we show how CPGs can directly be integrated as the Actor in an Actor-Critic formulation. Additionally, we demonstrate how this change permits us to integrate highly non-linear feedback directly from sensory perception to reshape the oscillators dynamics. Our results on a locomotion task using a single-leg hopper demonstrate that explicitly using the CPG as the Actor rather than as part of the environment results in a significant increase in the reward gained over time (6x more) compared with previous approaches. Furthermore, we show that our method without feedback reproduces results similar to prior work with feedback. Finally, we demonstrate how our closed-loop CPG progressively improves the hopping behaviour for longer training epochs relying only on basic reward functions.
In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution and learning, produces DPPNs to reconstruct an image. Our main result is that DPPNs can be evolved/trained to compress the weights of a denoising autoencoder from 157684 to roughly 200 parameters, while achieving a reconstruction accuracy comparable to a fully connected network with more than two orders of magnitude more parameters. The regularization ability of the DPPN allows it to rediscover (approximate) convolutional network architectures embedded within a fully connected architecture. Such convolutional architectures are the current state of the art for many computer vision applications, so it is satisfying that DPPNs are capable of discovering this structure rather than having to build it in by design. DPPNs exhibit better generalization when tested on the Omniglot dataset after being trained on MNIST, than directly encoded fully connected autoencoders. DPPNs are therefore a new framework for integrating learning and evolution.
A safety-critical measure of legged locomotion performance is a robots ability to track its desired time-varying position trajectory in an environment, which is herein termed as global-position tracking. This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3-D) bipedal robot walking. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Towards tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3-D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking.
This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the rimless wheel, and the compass gait, the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.
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