Spiking Neuromorphic Control for Periodic Orbits Stabilization in Underactuated Robots: A Greedy Lyapunov-Based Approach
Authors: Maksim Surov, Oleg Sumenkov
Organizations: The authors are with Mathematical Robotics Science Division, Sirius University of Science and Technology, Olympiyskiy Av. 1, Sirius, 354340 Russia
This work investigates the use of event-based spiking controllers, implemented as spiking neural networks, for trajectory tracking in underactuated robots. Specifically, we address the problem of stabilizing a prescribed periodic orbit. It is well known that, by applying the method of transverse linearization to the robot dynamics in a neighborhood of a periodic trajectory, the dynamics can be approximately described by a linear time-varying system with periodic coefficients (a periodic LTV system). The problem of orbital stabilization can therefore be reduced to stabilizing the trivial solution of this LTV system. We show that a previously proposed Lyapunov-based greedy design, originally developed for LTI systems, can also be extended to the corresponding linearized transverse dynamics, which take the form of a periodic LTV system. This enables the construction of a feedback controller for orbital stabilization of the robot. The effectiveness of the proposed method is demonstrated on the trajectory stabilization problem for the butterfly robot.
Figures & tables
Fig. 1: Schematic of the Butterfly robot. Generalized coordinates q≡(ϑ,φ) , where ϑ is the link orientation and φ is the angular position of the ball relative to the link; δ is the curve defining the shape of the link surface, and ρ is equidistant to it.
Fig. 2: Components of the desired solution x⋆(t) with the corresponding nominal control u⋆(t) .
Fig. 3: Transients of the transverse coordinates ξ . Control signal w (blue) and its low-pass-filtered counterpart (red).
Fig. 4: Reference signals ϑ⋆ , φ⋆ (red) and measured signals ϑ , φ (blue). Control input u (blue) and its low-pass-filtered counterpart (red).
Maintaining stable internal representations of continuous variables is fundamental for effective robotic control. Continuous attractor networks provide a biologically inspired mechanism for encoding such variables, yet neuromorphic realizations have rarely addressed proprioceptive estimation under resource constraints. This work introduces a spiking ring-attractor network representing a robot joint angle through self-sustaining population activity. Local excitation and broad inhibition support a stable activity bump, while velocity-modulated asymmetries drive its translation and boundary conditions confine motion within mechanical limits. The network reproduces smooth trajectory tracking and remains stable near joint limits, showing reduced drift and improved accuracy compared to unbounded models. Such compact hardware-compatible implementation preserves multi-second stability demonstrating a near-linear relationship between bump velocity and synaptic modulation.
Federica Ferrari, Flavia Davidhi, Bernard Maacaron +6
Istituto Italiano di Tecnologia, Genoa, Italy · Department of Neurosurgery, University Hospital Zürich, Switzerland · Institute of Neuroinformatics, Univ. of Zurich and ETH Zurich, Switzerland +3
This paper addresses orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model within a transverse-linearization framework. We show that the corresponding transverse linearization is unstable and not stabilizable by linear state feedback. Therefore, the standard linearization-based approach to orbital stabilization cannot be applied directly. The main contribution is a set of explicit and verifiable conditions that characterize when a controller design based on transverse linearization remains applicable. These conditions rely on the specific structure of the dynamics in a neighborhood of the motion and on the use of non-standard transverse coordinates for controller design and analysis. Numerical simulations illustrate the proposed design procedure.
Artem Angelchev-Shiryaev, Pavel E. Aleshin, Anton S. Shiriaev +2
Department of Industrial and Mechanical Sciences, Lund University, Lund, Sweden · Department of Information Technologies, Sirius University, Sirius, Russia · Department of Engineering Cybernetics, NTNU, Trondheim, Norway +1
Soft and soft-rigid hybrid robots are inherently underactuated and operate under tight actuator limits, making task-space control with stability guarantees challenging. Common nonlinear strategies for soft robots (e.g., those based on PD control) often rely on the assumption of full actuation with no actuator limits. This paper presents a general control framework for task-space regulation and tracking of underactuated soft robots under bounded inputs. The method enforces a rapidly exponentially stabilizing control Lyapunov function as a convex inequality constraint while simultaneously satisfying underactuated full-body dynamics and actuator bounds. We validate the approach in simulation on several platforms spanning increasing underactuation: a simple two link tendon-driven "finger", a trimmed helicoid manipulator, and a highly underactuated spiral robot. We compare against a number of baseline methods from the literature. Results show improved task-space accuracy and consistent Lyapunov convergence under input limits, achieving superior set-point and trajectory-tracking performance.
Huy Pham, Zach J. Patterson
Mechanical and Aerospace Engineering, Case Western Reserve University