We present an algorithm that generates walking motions for quadruped robots without the use of an explicit footstep planner by simultaneously optimizing over both the Center of Mass (CoM) trajectory and the footholds. Feasibility is achieved by imposing stability constraints on the CoM related to the Zero Moment Point and explicitly enforcing kinematic constraints between the footholds and the CoM position. Given a desired goal state, the problem is solved online by a Nonlinear Programming solver to generate the walking motion. Experimental trials show that the algorithm is able to generate walking gaits for multiple steps in milliseconds that can be executed on a real quadruped robot.

Sums-of-Squares optimization represents an important tool for the direct computation of a local Lyapunov function for a nonlinear dynamic system. Specifically, it can certify a sub-levelset of the cost-to-go from an optimal feedback controller like the Linear Quadratic Regulator (LQR), geometrically an ellipsoid in the state space, as Region of Attraction (ROA) of the closed-loop system. More complex robotic tasks however require switching control to first take the system into the ROA before invoking the LQR stabilizer. In this paper, we propose computationally efficient measures of the ROA distance based on quadratic and conic optimization to effectively supervise such a trajectory as it approaches the ROA. As a one-dimensional condensate of the multi-dimensional state trajectory, monitoring the ROA distance evolution allows us to early detect deviations, e.g. due to input saturation or time delay, in order to quickly take corrective action such as replanning. Importantly, computing the ROA distance adds only a small overhead on top of the ROA calculation itself and can be done concurrently.

Differential flatness is a property of certain systems that greatly simplifies the generation of optimal and dynamically feasible trajectories. Using a differentially flat model, there is no need to integrate the system dynamics to retrieve the states and the constraints of the optimization problem are simpler. Recently, the concept of partial differential flatness has been introduced covering a broader class of systems. In particular, it allows to reduce the need for integration by limiting it to a subset of the states. However, finding an analytical expression for the (partial) differential flatness requires the manipulation of the equations of motion in a very specific manner such that a series of properties are fulfilled. In general, finding such analytical model is not straightforward nor compatible with algorithmic models. In order to tackle this problem, in this paper we present a numerical method to find a (partially) differentially flat model of a system around a collection of states and inputs trajectories. We present results on three underactuated nonlinear systems (cart-pole, planar ballbot and a 3D quadrotor). As use case examples, we show online trajectory re-planning tasks. The validity of the trajectories obtained with the locally flat models is verified by forward integrating the original equations of motion together with an optimal stabilizer.

In this paper we present a feed forward controller to regulate the depth of laser incisions in soft tissue. Such a controller is compatible with the requirements of laser microsurgery, where space constraints limit the use of sensing devices. The controller is based on an inverse model that maps the desired incision depth to the required laser exposure time. This model is extracted from experimental data through the use of statistical learning methods. To prove the concept, the controller is implemented in a robot-assisted laser microsurgery system that enables precision control of exposure time and laser motion. The validity and the accuracy of the controller is verified experimentally on ex-vivo muscle tissue (chicken breast), revealing an RMSE of 0.12 mm for incisions ranging up to 1 mm. In addition, we demonstrate how the model can be used to implement the automatic ablation of entire volumes of tissue, through the superposition of controlled laser incisions.

This paper presents a method to estimate external forces exerted on a manipulator during motion, avoiding the use of a sensor. The method is based on task-oriented dynamics model learning and a robust disturbance state observer. The combination of both leads to an efficient torque observer that can be incorporated to any control scheme. The use of a learning-based approach avoids the need of analytical models of joints' friction or Coriolis dynamics effects.