We present a trajectory planning and control architecture for bipedal locomotion at a variety of speeds on a highly underactuated and compliant bipedal robot. A library of compliant walking trajectories are planned offline, and stored as compact arrays of polynomial coefficients for tracking online. The control implementation uses a floating-base inverse dynamics controller which generates dynamically consistent feedforward torques to realize walking using information obtained from the trajectory optimization. The effectiveness of the controller is demonstrated in simulation and on hardware for walking both indoors on flat terrain and over unplanned disturbances outdoors. Additionally, both the controller and optimization source code are made available on GitHub.
Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient.
The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.
Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties
The prolific rise in autonomous systems has led to questions regarding their safe instantiation in real-world scenarios. Failures in safety-critical contexts such as human-robot interactions or even autonomous driving can ultimately lead to loss of life. In this context, this paper aims to provide a method by which one can algorithmically test and evaluate an autonomous system. Given a black-box autonomous system with some operational specifications, we construct a minimax problem based on control barrier functions to generate a family of test parameters designed to optimally evaluate whether the system can satisfy the specifications. To illustrate our results, we utilize the Robotarium as a case study for an autonomous system that claims to satisfy waypoint navigation and obstacle avoidance simultaneously. We demonstrate that the proposed test synthesis framework systematically finds those sequences of events (tests) that identify points of system failure.
Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time barrier functions (DTBFs) and formulate sufficient conditions for finite time DTBF to study finite time convergence to a set. We then show that different LDTL mission/safety specifications can be cast as a set of invariance or finite time reachability problems. We demonstrate that the proposed method for safety-shield synthesis can be implemented online by a sequence of one-step greedy algorithms. We demonstrate the efficacy of the proposed method using experiments involving a team of robots.
This paper proposes a data-driven method for powered prosthesis control that achieves stable walking without the need for additional sensors on the human. The key idea is to extract the nominal gait and the human interaction information from motion capture data, and reconstruct the walking behavior with a dynamic model of the human-prosthesis system. The walking behavior of a human wearing a powered prosthesis is obtained through motion capture, which yields the limb and joint trajectories. Then a nominal trajectory is obtained by solving a gait optimization problem designed to reconstruct the walking behavior observed by motion capture. Moreover, the interaction force profiles between the human and the prosthesis are recovered by simulating the model following the recorded gaits, which are then used to construct a force tube that covers all the interaction force profiles. Finally, a robust Control Lyapunov Function (CLF) Quadratic Programming (QP) controller is designed to guarantee the convergence to the nominal trajectory under all possible interaction forces within the tube. Simulation results show this controller's improved tracking performance with a perturbed force profile compared to other control methods with less model information.
Understanding users' gait preferences of a lower-body exoskeleton requires optimizing over the high-dimensional gait parameter space. However, existing preference-based learning methods have only explored low-dimensional domains due to computational limitations. To learn user preferences in high dimensions, this work presents LineCoSpar, a human-in-the-loop preference-based framework that enables optimization over many parameters by iteratively exploring one-dimensional subspaces. Additionally, this work identifies gait attributes that characterize broader preferences across users. In simulations and human trials, we empirically verify that LineCoSpar is a sample-efficient approach for high-dimensional preference optimization. Our analysis of the experimental data reveals a correspondence between human preferences and objective measures of dynamic stability, while also highlighting inconsistencies in the utility functions underlying different users' gait preferences. This has implications for exoskeleton gait synthesis, an active field with applications to clinical use and patient rehabilitation.
Lower leg prostheses could improve the life quality of amputees by increasing comfort and reducing energy to locomote, but currently control methods are limited in modulating behaviors based upon the human's experience. This paper describes the first steps toward learning complex controllers for dynamical robotic assistive devices. We provide the first example of behavioral cloning to control a powered transfemoral prostheses using a Gated Recurrent Unit (GRU) based recurrent neural network (RNN) running on a custom hardware accelerator that exploits temporal sparsity. The RNN is trained on data collected from the original prosthesis controller. The RNN inference is realized by a novel EdgeDRNN accelerator in real-time. Experimental results show that the RNN can replace the nominal PD controller to realize end-to-end control of the AMPRO3 prosthetic leg walking on flat ground and unforeseen slopes with comparable tracking accuracy. EdgeDRNN computes the RNN about 240 times faster than real time, opening the possibility of running larger networks for more complex tasks in the future. Implementing an RNN on this real-time dynamical system with impacts sets the ground work to incorporate other learned elements of the human-prosthesis system into prosthesis control.