Development of Design Tools for the Optimization of Biologically Based Control Systems

As neurobiological knowledge about animal control of locomotion (Buschmann et al., 2015) and the sophistication of neurally-controlled robots (Dasgupta et al., 2015; Klein and Lewis, 2012; Schilling et al., 2013) simultaneously increase, design tools are needed to properly tune controllers. This is especially evident when one considers that the most detailed topological control networks are tuned by hand (Markin et al., 2016; Tóth et al., 2013), leading to function that only approximates what is desired, while the most effective robot studies either simplify the system (Scrivens et al., 2008) or make so many assumptions about network structure that much of the animal-like topology is eliminated (Dasgupta et al., 2015; Schilling et al., 2013). Therefore, the goal of this work is to produce design tools for neuromechanical models that enable the designer to search and optimize controller parameters to achieve desired behavior and guarantee stability. In my work, robots are modeled in AnimatLab, a neuromechanical simulator based on the Bullet physics engine (Cofer et al., 2010). To explore the parameters of such systems, I wrote a Matlab program called SimDesign (Szczecinski et al., 2016c). The user provides an AnimatLab simulation file, parameters to explore, and desired output, and SimDesign runs simulations in parallel to either sweep the specified parameters, or use optimization methods to automatically change them until the performance is deemed optimal. SimDesign is very useful for small projects that simulate quickly, or for exploring the system’s sensitivity to different parameters (Szczecinski et al., 2015c). However, it was evident that this approach is too slowfor tuning large simulations, and does not enable analysis of network properties like stability or robustness. In response to this challenge, new tools were developed to reduce runtime and/or more directly exploit network structure to provide quantitative insight into system function. The first of these, SteadyStateModel, used closed-form steady-state solutions of neurons, limbs, and actuators to approximate some network parameters. For instance, feedforward mapping networks were tuned by comparing their steady-state output to the desired output for a list of inputs (Szczecinski et al., 2015c). Similarly, muscle parameters can be tuned by using joint torques in worst-case kinematic configurations to approximate muscle forces, lengths, and velocities (Szczecinski et al., 2015c). I worked with a colleague to create a special version of SteadyStateModel that uses desired walking kinematics and inverse dynamics to tune muscle forces, pattern generator networks, and reflexes in a bottom-up fashion, resulting in animal-like walking in the hind legs of a simulation of a rat (Hunt et al., 2015) and a dog-like planar robot (Hunt, 2015). Steady State Model accelerated the parameter tuning of large models, but it did not reveal stability or robustness properties of the models. Therefore I developed another design tool, FeedbackDesign, with inspiration from my NASA Research Collaborator, Joshua Mehling. FeedbackDesign simulates open- and closed-loop neuromechanical controllers, finds equilibria and their stability, computes closed-form frequency responses, constructs Bode plots, and uses the results to provide stability margins (Szczecinski et al., 2016c). The network components are linear, but interface via saturating nonlinearities, and sequential nodes load one another. Therefore special care is required to compute the frequency response; in spite of these challenges, this method is still orders of magnitude faster than approximating the frequency response from subsequent time-domain simulations, representing a huge improvement in both speed and analysis power. Some network components, such as central pattern generators (CPGs), rely on nonlinearities to produce their intended behaviors, meaning that we cannot understand them by linearization alone. This limits the tools available, so to gain some intuition, I wrote another design tool called AnimatedNullclines. This program simulates CPG dynamics, and produces a phase portrait for each neuron at each time step, which it plays in sequence as an animation. This revealed the mechanism behind apparent bifurcations, enabling the identification of a bifurcation parameter (Szczecinski et al., 2015b). Numerically finding equilibria and their eigenvalues and eigenvectors confirmed that a CPG can oscillate (or not) in a variety of ways, which could be controlled by one parameter. The phase response curves (PRCs) reveal that the system responds to inputs differently depending on this parameter as well, revealing how the nervous system could adjust its sensitivity to sensory information in different scenarios (Szczecinski et al., 2016c). The goal of all of this work is to tune neural controllers precisely enough to control a robot. Therefore I oversaw the construction of MantisBot, a 29 degree-of-freedom, 13.3:1 scale robotic mantis controlled in real-time by neural simulations in AnimatLab (Szczecinski et al., 2015a). The design tools I developed directly informed the construction and tuning of the controller. Postural reflexes such as restepping when pushed or searching for ground contact were implemented as intermediate-level reflexes that exploit CPG dynamics (Szczecinski et al., 2015b). Later, I oversaw the construction of a simple head sensor that can locate a bright light as a faux-visual target (Getsy et al., 2016). This enabled visually-directed stepping with one leg with a distributed, sensory-coupled neural controller (Szczecinski et al., 2016b). My design tools effectively eliminated all hand-tuning of the controller. This represents significant progress in the field, eliminating the most painstaking part of the modeling process, guaranteeing stability of the resulting system, and producing precise enough motion to control a robot in real-time. My work has met its goal of making neural controllers more accessible to engineers by producing several analysis tools. It did not produce a one-size-fits-all solution to tuning neural controllers as was initially envisaged. My research found that some networks lend themselves to analytical derivations of equilibria and their stability, but large or nonlinear networks cannot be analyzed this way. Optimization techniques can be used to tune parameters in such a complex system by simulating its dynamics many times, but this is time-consuming. I conclude that a suite of specialized design tools that operate on different scales, used in a sequential manner is more useful than one program intended to tune the entire controller at once.