In this paper, a new control framework for an insect-scale flapping-wing vehicle is presented that exploits passive aerodynamic effects to stabilize the attitude dynamics. Many flapping-wing robotic flyers and flying insects share a common morphological feature in that the center of mass (CoM) is below the center of pressure (CoP), which makes the hovering configuration intrinsically unstable with open-loop control. Motivated by the fact that the CoM should be ahead of the CoP to ensure the longitudinal stability of the flight dynamics, a new coordinate system is proposed by placing a virtual control point (VCP) above the CoP. The dynamics in the new coordinates are derived using a near-identity diffeomorphism which admits a partial feedback linearization with stable zero dynamics. The behavior of the zero dynamics resembles the dynamics of a 3D pendulum with an aerodynamic damper. An adaptive controller is proposed to make the upright orientation almost globally asymptotically stable over a bounded uncertainty of the aerodynamic drag coefficient. The controller is evaluated in simulation with a Harvard RoboBee following a virtual control point reference trajectory.

Parallelism can be used to significantly increase the throughput of computationally expensive algorithms. With the widespread adoption of parallel computing platforms such as GPUs, it is natural to consider whether these architectures can benefit robotics researchers interested in solving trajectory optimization problems online. Differential Dynamic Programming (DDP) algorithms have been shown to achieve some of the best timing performance in robotics tasks by making use of optimized dynamics methods and CPU multi-threading. This paper aims to analyze the benefits and tradeoffs of higher degrees of parallelization using a multiple-shooting variant of DDP implemented on a GPU. We describe our implementation strategy and present results demonstrating its performance compared to an equivalent multi-threaded CPU implementation using several benchmark control tasks. Our results suggest that GPU-based solvers can offer increased per-iteration computation time and faster convergence in some cases, but in general tradeoffs exist between convergence behavior and degree of parallelism.

Contact interactions are central to robot manipulation and locomotion behaviors. State estimation techniques that explicitly capture the dynamics of contact offer the potential to reduce estimation errors from unplanned contact events and improve closed-loop control performance. This is particularly true in highly dynamic situations where common simplifications like no-slip or quasi-static sliding are violated. Incorporating contact constraints requires care to address the numerical challenges associated with discontinuous dynamics, which make straightforward application of derivative-based techniques such as the Extended Kalman Filter impossible. In this paper, we derive an approximate maximum a posteriori estimator that can handle rigid body contact by explicitly imposing contact constraints in the observation update. We compare the performance of this estimator to an existing state-of-the-art Unscented Kalman Filter designed for estimation through contact and demonstrate the scalability of the approach by estimating the state of a 20-DOF bipedal robot in realtime.

Planning locomotion trajectories for legged microrobots is challenging. This is because of their complex morphology, high frequency passive dynamics, and discontinuous contact interactions with their environment. Consequently, such research is often driven by time-consuming experimental methods. As an alternative, we present a framework for systematically modeling, planning, and controlling legged microrobots. We develop a three- dimensional dynamic model of a 1.5 g quadrupedal microrobot with complexity (e.g., number of degrees of freedom) similar to larger-scale legged robots. We then adapt a recently developed variational contact-implicit trajectory optimization method to generate feasible whole-body locomotion plans for this microrobot, and demonstrate that these plans can be tracked with simple joint-space controllers. We plan and execute periodic gaits at multiple stride frequencies and on various surfaces. These gaits achieve high per-cycle velocities, including a maximum of 10.87 mm/cycle, which is 15% faster than previously measured for this microrobot. Furthermore, we plan and execute a vertical jump of 9.96 mm, which is 78% of the microrobot’s center-of- mass height. To the best of our knowledge, this is the first end-to-end demonstration of planning and tracking whole-body dynamic locomotion on a millimeter-scale legged microrobot.

The increasing capabilities of exoskeletons and powered prosthetics for walking assistance have paved the way for more sophisticated and individualized control strategies. In response to this opportunity, recent work on human-in-the-loop optimization has considered the problem of automatically tuning control parameters based on realtime physiological measurements. However, the common use of metabolic cost as a performance metric creates significant experimental challenges due to its long measurement times and low signal-to-noise ratio. We evaluate the use of Bayesian optimization—a family of sample-efficient, noise-tolerant, and global optimization methods—for quickly identifying near-optimal control parameters. To manage experimental complexity and provide comparisons against related work, we consider the task of minimizing metabolic cost by optimizing walking step frequencies in unaided human subjects. Compared to an existing approach based on gradient descent, Bayesian optimization identified a near-optimal step frequency with a faster time to convergence (12 minutes, p < 0.01), smaller inter-subject variability in convergence time (± 2 minutes, p < 0.01), and lower overall energy expenditure (p < 0.01).