Enric Celaya

IROS Conference 2022 Conference Paper

A Legendre-Gauss Pseudospectral Collocation Method for Trajectory Optimization in Second Order Systems

• Siro Moreno-Martín
• Lluís Ros
• Enric Celaya

Pseudospectral collocation methods have proven to be powerful tools to solve optimal control problems. While these methods generally assume the dynamics is given in the first order form $x$ = f(x, u, t), where $x$ is the state and $u$ is the control vector, robotic systems are typically governed by second order ODEs of the form $q$ = g(q, q, u, t), where $q$ is the configuration. To convert the second order ODE into a first order one, the usual approach is to introduce a velocity variable $v$ and impose its coincidence with the time derivative of q. Lobatto methods grant this constraint by construction, as their polynomials describing the trajectory for $v$ are the time derivatives of those for q, but the same cannot be said for the Gauss and Radau methods. This is problematic for such methods, as then they cannot guarantee that $q$ = g(q, q, u, t) at the collocation points. On their negative side, Lobatto methods cannot be used to solve initial value problems, as given the values of $u$ at the collocation points they generate an overconstrained system of equations for the states. In this paper, we propose a Legendre-Gauss collocation method that retains the advantages of the usual Lobatto, Gauss, and Radau methods, while avoiding their shortcomings. The collocation scheme we propose is applicable to solve initial value problems, preserves the consistency between the polynomials for $v$ and q, and ensures that $q$ = g(q, q, u, t) at the collocation points.

ECAI Conference 2004 Conference Paper

Learning Model Free Motor Control

• Alejandro Agostini
• Enric Celaya

IROS Conference 2004 Conference Paper

Trajectory tracking control of a rotational joint using feature-based categorization learning

• Alejandro Agostini
• Enric Celaya

Real world robot applications have to cope with large variations in the operating conditions due to the variability and unpredictability of the environment and its interaction with the robot. Performing an adequate control using conventional control techniques, that require the model of the plant and some knowledge about the influence of the environment, could be almost impossible. An alternative to traditional control techniques is to use an automatic learning system that uses previous experience to learn an adequate control policy. Learning by experience has been formalized in the field of reinforcement learning. But the application of reinforcement learning techniques in complex environments is only feasible when some generalization can be made in order to reduce the required amount of experience. This work presents an algorithm that performs a kind of generalization called categorization. This algorithm is able to perform efficient generalization of the observed situations, and learn accurate control policies in a short time without any previous knowledge of the plant and without the need of any kind of traditional control technique. Its performance is evaluated on the trajectory tracking control with simulated DC motors and compared with PID systems specifically tuned for the same problem.

ICRA Conference 1996 Conference Paper

Control of a six-legged robot walking on abrupt terrain

• Enric Celaya
• Josep M. Porta

Legged robots are well suited to walk on difficult terrains at the expense of requiring complex control systems to walk even on flat surfaces. But simply walking on a flat surface is not worth using a legged robot. It should be assumed that walking on abrupt terrain is the typical situation for a legged robot. With this premise in mind, we have developed a robust controller for a six-legged robot that allows it to walk over difficult terrains in an autonomous way, with a limited use of sensory information (no vision is involved). This walk controller can be driven by an upper level which need not be concerned about the details of foot placement or leg movements, taking care only of high level aspects such as global speed and direction.

ECAI Conference 1990 Conference Paper

Finding Object Configurations that Satisfy Spatial Relationships

• Enric Celaya
• Carme Torras