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Modern applications of robotics typically involve a robot control system with an inner PI (proportional-integral) or PID (proportional-integral-derivative) control loop and an outer user-specified control loop. The existing outer loop…
In this report, we apply the proposed "para-model" framework in order to control the trajectory of a dynamical system-based robot. The optimization of the dynamical performances in closed-loop is performed using a derivative-free…
Trajectory optimization is a fundamental problem in robotics. While optimization of continuous control trajectories is well developed, many applications require both discrete and continuous, i.e., hybrid, controls. Finding an optimal…
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid version of Pontryagin's maximum principle is presented. This…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
Differential dynamic programming (DDP) is a direct single shooting method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit…
Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control…
Robotic manipulation demands precise control over both contact forces and motion trajectories. While force control is essential for achieving compliant interaction and high-frequency adaptation, it is limited to operations in close…
Soft robots are gaining popularity thanks to their intrinsic safety to contacts and adaptability. However, the potentially infinite number of Degrees of Freedom makes their modeling a daunting task, and in many cases only an approximated…
Dynamic motions are a key feature of robotic arms, enabling them to perform tasks quickly and efficiently. Soft continuum manipulators do not currently consider dynamic parameters when operating in task space. This shortcoming makes…
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…
Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
Stabilizing legged robot locomotion on a dynamic rigid surface (DRS) (i.e., rigid surface that moves in the inertial frame) is a complex planning and control problem. The complexity arises due to the hybrid nonlinear walking dynamics…
Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address…
We present a new framework for prioritized multi-task motion-force control of fully-actuated robots. This work is established on a careful review and comparison of the state of the art. Some control frameworks are not optimal, that is they…