Control Systems and Robotics Outreach to Middle-school Girls: Approach, Results, and Suggestions

We conducted a three-day outreach camp focused on control systems and robotics for 8th grade girls from economically disadvantaged families. The overall objective of the camp was motivating the young girls to consider pursuing a career in engineering and sciences. The main focus of the camp were hands-on labs using LEGO Mindstorms EV3 kit. Students learned about programming, sensors, motors and put their skills to test by creating a mobile robot that took part in three contests: car racing, line following, and parallel parking. A pre- and post-camp survey indicated that although program did not predominantly change the girls’ excitement towards careers in engineering and sciences, it increased the girls’ knowledge and excitement towards robotics and control systems. Our results indicate that short camps help kindle the interests of young girls, but are not able to sway them to take on engineering/science careers. In the latter case, we hypothesize that long-term STEM-based programs (e.g., a quarter or year-long robotics course) might be more effective.Cockrell School of Engineerin

Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping

Inspired by biological control synergies, wherein fixed groups of muscles are activated in a coordinated fashion to perform tasks in a stable way, we present an analogous control approach for the stabilization of legged robots and apply it to a model of running. Our approach is based on the step-to-step notion of stability, also known as orbital stability, using an orbital control Lyapunov function. We map both the robot state at a suitably chosen Poincaré section (an instant in the locomotion cycle such as the mid-flight phase) and control actions (e.g., foot placement angle, thrust force, braking force) at the current step, to the robot state at the Poincaré section at the next step. This map is used to find the control action that leads to a steady state (nominal) gait. Next, we define a quadratic Lyapunov function at the Poincaré section. For a range of initial conditions, we find control actions that would minimize an energy metric while ensuring that the Lyapunov function decays exponentially fast between successive steps. For the model of running, we find that the optimization reveals three distinct control synergies depending on the initial conditions: (1) foot placement angle is used when total energy is the same as that of the steady state (nominal) gait; (2) foot placement angle and thrust force are used when total energy is less than the nominal; and (3) foot placement angle and braking force are used when total energy is more than the nominal

A Simple Controller for Omnidirectional Trotting of Quadrupedal Robots: Command Following and Waypoint Tracking

For autonomous legged robots to be deployed in practical scenarios, they need to perform perception, motion planning, and locomotion control. Since robots have limited computing capabilities, it is important to realize locomotion control with simple controllers that have modest calculations. The goal of this paper is to create computational simple controllers for locomotion control that can free up computational resources for more demanding computational tasks, such as perception and motion planning. The controller consists of a leg scheduler for sequencing a trot gait with a fixed step time; a reference trajectory generator for the feet in the Cartesian space, which is then mapped to the joint space using an analytical inverse; and a joint controller using a combination of feedforward torques based on static equilibrium and feedback torque. The resulting controller enables velocity command following in the forward, sideways, and turning directions. With these three velocity command following-modes, a waypoint tracking controller is developed that can track a curve in global coordinates using feedback linearization. The command following and waypoint tracking controllers are demonstrated in simulation and on hardware

Event-Based, Intermittent, Discrete Adaptive Control for Speed Regulation of Artificial Legs

For artificial legs that are used in legged robots, exoskeletons, and prostheses, it suffices to achieve velocity regulation at a few key instants of swing rather than tight trajectory tracking. Here, we advertise an event-based, intermittent, discrete controller to enable set-point regulation for problems that are traditionally posed as trajectory following. We measure the system state at prior-chosen instants known as events (e.g., vertically downward position), and we turn on the controller intermittently based on the regulation errors at the set point. The controller is truly discrete, as these measurements and controls occur at the time scale of the system to be controlled. To enable set-point regulation in the presence of uncertainty, we use the errors to tune the model parameters. We demonstrate the method in the velocity control of an artificial leg, a simple pendulum, with up to 50% mass uncertainty. Starting with a 100% regulation error, we achieve velocity regulation of up to 10% in about five swings with only one measurement per swing

One-Step Deadbeat Control of a 5-Link Biped Using Data-Driven Nonlinear Approximation of the Step-to-Step Dynamics

For bipedal robots to walk over complex and constrained environments (e.g., narrow walkways, stepping stones), they have to meet precise control objectives of speed and foot placement at every single step. This control that achieves the objectives precisely at every step is known as one-step deadbeat control. The high dimensionality of bipedal systems and the under-actuation (number of joint exceeds the actuators) presents a formidable computational challenge to achieve real-time control. In this paper, we present a computationally efficient method for one-step deadbeat control and demonstrate it on a 5-link planar bipedal model with 1 degree of under-actuation. Our method uses computed torque control using the 4 actuated degrees of freedom to decouple and reduce the dimensionality of the stance phase dynamics to a single degree of freedom. This simplification ensures that the step-to-step dynamics are a single equation. Then using Monte Carlo sampling, we generate data for approximating the step-to-step dynamics followed by curve fitting using a control affine model and a Gaussian process error model. We use the control affine model to compute control inputs using feedback linearization and fine tune these using iterative learning control using the Gaussian process error enabling one-step deadbeat control. We demonstrate the approach in simulation in scenarios involving stabilization against perturbations, following a changing velocity reference, and precise foot placement. We conclude that computed torque control-based model reduction and sampling-based approximation of the step-to-step dynamics provides a computationally efficient approach for real-time one-step deadbeat control of complex bipedal systems

Optimal Control of a 5-Link Biped Using Quadratic Polynomial Model of Two-Point Boundary Value Problem

To walk over constrained environments, bipedal robots must meet concise control objectives of speed and foot placement. The decisions made at the current step need to factor in their effects over a time horizon. Such step-to-step control is formulated as a two-point boundary value problem (2-BVP). As the dimensionality of the biped increases, it becomes increasingly difficult to solve this 2-BVP in real-time. The common method to use a simple linearized model for real-time planning followed by mapping on the high dimensional model cannot capture the nonlinearities and leads to potentially poor performance for fast walking speeds. In this paper, we present a framework for real-time control based on using partial feedback linearization (PFL) for model reduction, followed by a data-driven approach to find a quadratic polynomial model for the 2-BVP. This simple step-to-step model along with constraints is then used to formulate and solve a quadratically constrained quadratic program to generate real-time control commands. We demonstrate the efficacy of the approach in simulation on a 5-link biped following a reference velocity profile and on a terrain with ditches. A video is here: https://youtu.be/-UL-wkv4XF8