Sergei Savin

This work presents a sampling-based Quadratic Stability Control (QSC) framework for nonlinear mechanical systems with parametric uncertainty and compares it with a nominal Linear Quadratic Regulator (LQR). The proposed method synthesizes a single state-feedback gain by enforcing a common quadratic Lyapunov condition over a finite set of locally linearized models sampled in state and parameter space. A systematic numerical study evaluates the effects of the number of sampled models, state sampling radius, parameter uncertainty, and actuator configuration. Performance is assessed using trajectory mean-squared error, final position error, and offline controller-synthesis time. The results show that QSC has higher position error than nominal LQR at 5% uncertainty but lower error at 10% and 15% across five independently sampled designs, with greater force effort while maintaining comparable nominal performance. The common quadratic certificate covers the sampled models and their convex hull, not the full continuous nonlinear domain. These benefits are obtained at the cost of higher offline semidefinite-programming complexity.

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

This paper proposes a method for simultaneously planning a path and a sequence of deformations for a tensegrity drone. Previous work in the field required the use of bounding surfaces, making the planning more conservative. The proposed method takes advantage of the need to use mixed-integer variables in choosing the drone path (using big-M relaxation) to simultaneously choose the configuration of the drone, eliminating the need to use semidefinite matrices to encode configurations, as was done previously. The numerical properties of the algorithm are demonstrated in numerical studies. To show the viability of tensegrity drones, the first tensegrity quadrotor Tensodrone was build. The Tensodrone is based on a six-bar tensegrity structure that is inherently compliant and can withstand crash landings and frontal collisions with obstacles. This makes the robot safe for the humans around it and protects the drone itself during aggressive maneuvers in constrained and cluttered environments, a feature that is becoming increasingly important for challenging applications that include cave exploration and indoor disaster response.

The development of deformable drones is of high importance but presents significant challenges. Such drones can be based on tensegrity structures, which leaves open the questions of configuration-space path planning for such robots. In this paper we propose a method that takes advantage of a simplified encoding of the drone’s shape, allowing to turn the path planning into a sequence of semidefinite programs. The mapping from the simplified description and the actual tensegrity configuration is done via a data-driven method, using a pre-computed dataset of statically stable configurations and their outer Löwner-John ellipsoids, as well as eigendecompositions of the ellipsoid matrices. Together it allows rapid containment check, whose computational cost depends linearly on the number of dataset entries. Thus, the proposed method offloads computationally-intensive parts to the offline dataset generation procedure, speeding up the algorithm execution.

In this paper, an orthogonal decomposition-based state observer for systems with explicit constraints is proposed. State observers have been an integral part of robotic systems, reflecting the practicality and effectiveness of the dynamic state feedback control, but the same methods are lacking for the systems with explicit mechanical constraints, where observer designs have been proposed only for special cases of such systems, with relatively restrictive assumptions. This work aims to provide an observer design framework for a general case linear time-invariant system with explicit constraints, by finding lower-dimensional subspaces in the state space, where the system is observable while giving sufficient information for both feedback and feed-forward control. We show that the proposed formulation recovers minimal coordinate representation when it is sufficient for the control law generation and retains non-minimal coordinates when those are required for the feed-forward control law. The proposed observer is tested on a flywheel inverted pendulum and on a quadruped robot Unitree A1.

This paper focuses on the topic of contact reaction prediction for walking robots, namely on the analysis of performances on different structures of the machine-learning-based predictors. Predicting reaction forces is important due to the fact that it can allow us to retrieve a simplified model of the contact scenario, as was proposed in the literature preciously. This allows to turn the problem of contact model identification into a data collection and processing problem. In order to do it effectively, both a data compression (feature extraction) and regression strategies might be used. This research provides an analysis of both with respect to the discussed problem.