Locomotion Control
Objectives and Significance
This basic research aims to establish a general theory for designing feedback control mechanisms to drive robotic systems that swim like fishes or crawl like snakes. The design method will enable propulsion with agility and energy efficiency. The control algorithm is inspired by the central pattern generator (CPG) --- neuronal circuits that command muscle contractions to achieve rhythmic body movements during animal locomotion. The CPG is an interconnection of multiple neurons with simple individual dynamics, exhibiting a collective behavior perceived as a pattern. What makes CPGs an attractive object for engineering applications is its ability to adaptively choose the pattern of body oscillation appropriate for varying environments. This exploratory research will investigate the potential of the CPG architecture to provide a viable foundation for a new system design methodology to achieve coordinated oscillations of mechanical systems by feedback control. Understanding of the mechanisms underlying emergent behaviors of CPGs could provide a central idea for innovative design of engineered systems with new functionalities. A theory that relates local interactions to the resulting global pattern would help identify, predict, or avoid, for instance, traffic congestion and instability in power grids. Synergistic effects are also expected between neuroscience and control engineering.
Resuts
We proposed a general framework for CPG-based control design. Each neuron is modeled by a threshold nonlinearity psi followed by a low pass filter F(s), the CPG is a network of such neurons with connectivity matrix M, and the controller is specified by adding input/output channels to the CPG as shown below. The design problem is to find the controller parameters such that the closed-loop system with the plant P(s) has a stable limit cycle of prescribed frequency, amplitudes, and phases. With the harmonic balance method, the problem is reduced to an eigenstructure assignment, which can readily be solved if no additional requirement is imposed. When the CPG is required to have a distributed structure, the design can be reduced to a numerical search to meet matrix inequality constraints. In this design framework, it is possible to formulate the search to achieve multiple gaits under multiple environment conditions, embedding the adaptivity property in the control system. To illustrate the method, a six-link undulatory swimmer is considered and a CPG controller with coupled five-segment oscillators with local sensing/actuation is designed to achieve two gaits in the nominal water and perturbed viscosity environments. The design is based on a linear model of the swimmer, but closed-loop simulation with the nonlinear swimmer demonstrates effectiveness of the design for adaptive gait transition.
Body snapshots in water (left) and high viscosity fluid (right)
Transition from water to high viscosity fluid at t=2
phi = joint angles, q = CPG states
u = joint torques, v = swim speed
We have also developed a simple control scheme based on the reciprocal inhibition oscillation (RIO) to actuate one DOF to excite the resonance mode of a multi-DOF system. The resonance entrainment method was applied to control a tensegrity swimmer. The main body is made of a tensegrity structure consisting of rigid bars and a pair of flexible cables driven by a motor. The body is hung under a rail and can slide along when the tail fin, submerged into water, flips around and generates thrust. The controller successfully entrained to a resonance mode of the fluid-structure interaction system and achieved efficient swimming. This work is done in collaboration with BIER Lab at the University of Virginia.
References
Serpentine Locomotion with Robotic Snakes
M. Saito, M. Fukaya, and T. Iwasaki, IEEE Control Systems Magazine, vol.22, no.1, pp.64-81, 2002.
Oscillation, Orientation, and Locomotion of Underactuated Multilink Mechanical Systems
L. Zhu, Z. Chen, and T. Iwasaki, IEEE Transactions on Control Systems Technology, vol.21, no.5, pp.1537-1548, 2013.
Neural control for coordinated natural oscillation patterns
Z. Chen, T. Iwasaki, and L. Zhu, Systems & Control Letters, vol.62, pp.693-698, 2013.
Central Pattern Generator Control of a Tensegrity Swimmer
T. Bliss, T. Iwasaki, and H. Bart-Smith, IEEE/ASME Transactions on Mechatronics, vol.18, no.2, pp.586-597, 2013.
Z. Chen, T. Iwasaki, and L. Zhu, IEEE Transactions on Control Systems Technology, vol.23, no.4, pp.1294-1306, 2015.
Design of Controllers with Distributed CPG Architecture for Adaptive Oscillations
A. Wu and T. Iwasaki, IEEE Transactions on Control Systems Technology (submitted).
Central pattern generator control of a tensegrity based swimmer
Tom Bliss, Ph.D Dissertation, University of Virginia, September 2011
Pattern Formation via Eigenstructure Assignment
Andy Wu, Ph.D Dissertation, UCLA, June 2016