Teaching Robots to Span the Space of Functional Expressive Motion

Our goal is to enable robots to perform functional tasks in emotive ways, be it in response to their users' emotional states, or expressive of their confidence levels. Prior work has proposed learning independent cost functions from user feedback for each target emotion, so that the robot may optimize it alongside task and environment specific objectives for any situation it encounters. However, this approach is inefficient when modeling multiple emotions and unable to generalize to new ones. In this work, we leverage the fact that emotions are not independent of each other: they are related through a latent space of Valence-Arousal-Dominance (VAD). Our key idea is to learn a model for how trajectories map onto VAD with user labels. Considering the distance between a trajectory's mapping and a target VAD allows this single model to represent cost functions for all emotions. As a result 1) all user feedback can contribute to learning about every emotion; 2) the robot can generate trajectories for any emotion in the space instead of only a few predefined ones; and 3) the robot can respond emotively to user-generated natural language by mapping it to a target VAD. We introduce a method that interactively learns to map trajectories to this latent space and test it in simulation and in a user study. In experiments, we use a simple vacuum robot as well as the Cassie biped.

Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we cast the computation of region-ofattraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.

Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments

Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class $\mathcal{K}$ function in CBFs usually needs to be tuned manually in order to balance the trade-off between performance and safety for each environment. However, this process is often heuristic and can become intractable for high relative-degree systems. Moreover, it prevents the CBF-QP from generalizing to different environments in the real world. By embedding the optimization procedure of the CBF-QP as a differentiable layer within a deep learning architecture, we propose a differentiable optimization-based safety-critical control framework that enables generalization to new environments with forward invariance guarantees. Finally, we validate the proposed control design with 2D double and quadruple integrator systems in various environments.

Competitive Car Racing with Multiple Vehicles using a Parallelized Optimization with Safety Guarantee

This paper presents a novel planning and control strategy for competing with multiple vehicles in a car racing scenario. The proposed racing strategy switches between two modes. When there are no surrounding vehicles, a learning-based model predictive control (MPC) trajectory planner is used to guarantee that the ego vehicle achieves better lap timing. When the ego vehicle is competing with other surrounding vehicles to overtake, an optimization-based planner generates multiple dynamically-feasible trajectories through parallel computation. Each trajectory is optimized under a MPC formulation with different homotopic Bezier-curve reference paths lying laterally between surrounding vehicles. The time-optimal trajectory among these different homotopic trajectories is selected and a low-level MPC controller with obstacle avoidance constraints is used to guarantee system safety-critical performance. The proposed algorithm has the capability to generate collision-free trajectories and track them while enhancing the lap timing performance with steady low computational complexity, outperforming existing approaches in both timing and performance for a car racing environment. To demonstrate the performance of our racing strategy, we simulate with multiple randomly generated moving vehicles on the track and test the ego vehicle's overtake maneuvers.

Quadrupedal Robotic Guide Dog with Vocal Human-Robot Interaction

Guide dogs play a critical role in the lives of many, however training them is a time- and labor-intensive process. We are developing a method to allow an autonomous robot to physically guide humans using direct human-robot communication. The proposed algorithm will be deployed on a Unitree A1 quadrupedal robot and will autonomously navigate the person to their destination while communicating with the person using a speech interface compatible with the robot. This speech interface utilizes cloud based services such as Amazon Polly and Google Cloud to serve as the text-to-speech and speech-to-text engines.

A Fast Computational Optimization for Control and Trajectory Planning for Obstacle Avoidance between Polytopes

Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.

Vision-aided Dynamic Quadrupedal Locomotion on Discrete Terrain using Motion Libraries

In this paper, we present a framework rooted in control and planning that enables quadrupedal robots to traverse challenging terrains with discrete footholds using visual feedback. Navigating discrete terrain is challenging for quadrupeds because the motion of the robot can be aperiodic, highly dynamic, and blind for the hind legs of the robot. Additionally, the robot needs to reason over both the feasible footholds as well as robot velocity by speeding up and slowing down at different parts of the terrain. We build an offline library of periodic gaits which span two trotting steps on the robot, and switch between different motion primitives to achieve aperiodic motions of different step lengths on an A1 robot. The motion library is used to provide targets to a geometric model predictive controller which controls stance. To incorporate visual feedback, we use terrain mapping tools to build a local height map of the terrain around the robot using RGB and depth cameras, and extract feasible foothold locations around both the front and hind legs of the robot. Our experiments show a Unitree A1 robot navigating multiple unknown, challenging and discrete terrains in the real world.

A Fast Computational Optimization for Optimal Control and Trajectory Planning for Obstacle Avoidance between Polytopes

Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.