An application of Lyapunov stability analysis to improve the performance of NARMAX models

Previously we presented a novel approach to program a robot controller based on system identification and robot training techniques. The proposed method works in two stages: first, the programmer demonstrates the desired behaviour to the robot by driving it manually in the target environment. During this run, the sensory perception and the desired velocity commands of the robot are logged. Having thus obtained training data we model the relationship between sensory readings and the motor commands of the robot using ARMAX/NARMAX models and system identification techniques. These produce linear or non-linear polynomials which can be formally analysed, as well as used in place of “traditional robot” control code.In this paper we focus our attention on how the mathematical analysis of NARMAX models can be used to understand the robot’s control actions, to formulate hypotheses and to improve the robot’s behaviour. One main objective behind this approach is to avoid trial-and-error refinement of robot code. Instead, we seek to obtain a reliable design process, where program design decisions are based on the mathematical analysis of the model describing how the robot interacts with its environment to achieve the desired behaviour. We demonstrate this procedure through the analysis of a particular task in mobile robotics: door traversal.     

Robot control code generation by task demonstration in a dynamic environment

Within mobile robotics, one of the most dominant relationships to consider when implementing robot control code is the one between the robot’s sensors and its motors. When implementing such a relationship, efficiency and reliability are of crucial importance. The latter aspects often prove challenging due to the complex interaction between a robot and the environment in which it exists, frequently resulting in a time consuming iterative process where control code is redeveloped and tested many times before obtaining an optimal controller. In this paper, we address this challenge by implementing an alternative approach to control code generation, which first identifies the desired robot behaviour and represents the sensor-motor task algorithmically through system identification using the NARMAX modelling methodology. The control code is generated by task demonstration, where the sensory perception and velocities are logged and the relationship that exists between them is then modelled using system identification. This approach produces transparent control code through non-linear polynomial equations that can be mathematically analysed to obtain formal statements regarding specific inputs/outputs. We demonstrate this approach to control code generation and analyse its performance in dynamic environments.     

Exploiting submodular value functions for scaling up active perception

In active perception tasks, an agent aims to select sensory actions that reduce its uncertainty about one or more hidden variables. For example, a mobile robot takes sensory actions to efficiently navigate in a new environment. While partially observable Markov decision processes (POMDPs) provide a natural model for such problems, reward functions that directly penalize uncertainty in the agent’s belief can remove the piecewise-linear and convex (PWLC) property of the value function required by most POMDP planners. Furthermore, as the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially with it, making POMDP planning infeasible with traditional methods. In this article, we address a twofold challenge of modeling and planning for active perception tasks. We analyze \(\rho \)POMDP and POMDP-IR, two frameworks for modeling active perception tasks, that restore the PWLC property of the value function. We show the mathematical equivalence of these two frameworks by showing that given a \(\rho \)POMDP along with a policy, they can be reduced to a POMDP-IR and an equivalent policy (and vice-versa). We prove that the value function for the given \(\rho \)POMDP (and the given policy) and the reduced POMDP-IR (and the reduced policy) is the same. To efficiently plan for active perception tasks, we identify and exploit the independence properties of POMDP-IR to reduce the computational cost of solving POMDP-IR (and \(\rho \)POMDP). We propose greedy point-based value iteration (PBVI), a new POMDP planning method that uses greedy maximization to greatly improve scalability in the action space of an active perception POMDP. Furthermore, we show that, under certain conditions, including submodularity, the value function computed using greedy PBVI is guaranteed to have bounded error with respect to the optimal value function. We establish the conditions under which the value function of an active perception POMDP is guaranteed to be submodular. Finally, we present a detailed empirical analysis on a dataset collected from a multi-camera tracking system employed in a shopping mall. Our method achieves similar performance to existing methods but at a fraction of the computational cost leading to better scalability for solving active perception tasks.     

Auditory learning: a developmental method

Motivated by the human autonomous development process from infancy to adulthood, we have built a robot that develops its cognitive and behavioral skills through real-time interactions with the environment. We call such a robot a developmental robot. In this paper, we present the theory and the architecture to implement a developmental robot and discuss the related techniques that address an array of challenging technical issues. As an application, experimental results on a real robot, self-organizing, autonomous, incremental learner (SAIL), are presented with emphasis on its audition perception and audition-related action generation. In particular, the SAIL robot conducts the auditory learning from unsegmented and unlabeled speech streams without any prior knowledge about the auditory signals, such as the designated language or the phoneme models. Neither available before learning starts are the actions that the robot is expected to perform. SAIL learns the auditory commands and the desired actions from physical contacts with the environment including the trainers.     

Task Transfer by a Developmental Robot

Scaffolding is a process of transferring learned skills to new and more complex tasks through arranged experience in open-ended development. In this paper, we propose a developmental learning architecture that enables a robot to transfer skills acquired in early learning settings to later more complex task settings. We show that a basic mechanism that enables this transfer is sequential priming combined with attention, which is also the driving mechanism for classical conditioning, secondary conditioning, and instrumental conditioning in animal learning. A major challenge of this work is that training and testing must be conducted in the same program operational mode through online, real-time interactions between the agent and the trainers. In contrast with former modeling studies, the proposed architecture does not require the programmer to know the tasks to be learned and the environment is uncontrolled. All possible perceptions and actions, including the actual number of classes, are not available until the programming is finished and the robot starts to learn in the real world. Thus, a predesigned task-specific symbolic representation is not suited for such an open-ended developmental process. Experimental results on a robot are reported in which the trainer shaped the behaviors of the agent interactively, continuously, and incrementally through verbal commands and other sensory signals so that the robot learns new and more complex sensorimotor tasks by transferring sensorimotor skills learned in earlier periods of open-ended development     

Active object tracking using context estimation: handling occlusions and detecting missing targets

When performing visual servoing or object tracking tasks, active sensor planning is essential to keep targets in sight or to relocate them when missing. In particular, when dealing with a known target missing from the sensor’s field of view, we propose using prior knowledge related to contextual information to estimate its possible location. To this end, this study proposes a Dynamic Bayesian Network that uses contextual information to effectively search for targets. Monte Carlo particle filtering is employed to approximate the posterior probability of the target’s state, from which uncertainty is defined. We define the robot’s utility function via information theoretic formalism as seeking the optimal action which reduces uncertainty of a task, prompting robot agents to investigate the location where the target most likely might exist. Using a context state model, we design the agent’s high-level decision framework using a Partially-Observable Markov Decision Process. Based on the estimated belief state of the context via sequential observations, the robot’s navigation actions are determined to conduct exploratory and detection tasks. By using this multi-modal context model, our agent can effectively handle basic dynamic events, such as obstruction of targets or their absence from the field of view. We implement and demonstrate these capabilities on a mobile robot in real-time.

     

A voice-activated robot with artificial intelligence

In this paper, a voice activated robot arm with intelligence is presented. The robot arm is controlled with natural connected speech input. The language input allows a user to interact with the robot in terms which are familiar to most people. The advantages of speech activated robots are hands-free and fast data input operations. The proposed robot is capable of understanding the meaning of natural language commands. After interpreting the voice commands a series of control data for performing a tasks are generated. Finally the robot actually performs the task. Artificial Intelligence techniques are used to make the robot understand voice commands and act in the desired mode. It is also possible to control the robot using the keyboard input mode.     

Force-guided motions of a 6-d.o.f. industrial robot with a joint space approach

This article deals with the interaction between humans and industrial robots, more specifically with the new design and implementation of an algorithm for force-guided motions of a 6-d.o.f. robot. It may be used to comfortably teach positions without using any teaching pendant or for some assistance tasks. For this purpose, from readings of the force/torque sensor mounted in the robot wrist, the gravity forces and torques first have to be eliminated. To control the robot in joint space, it is then convenient to transform the external force and torque values from Cartesian space into joint space using the manipulator transposed Jacobian. This is why with the present approach the Jacobian matrix of the robot used was calculated. Now, from the computed joint torques, suitable position commands of the robot arm can be generated to obtain the desired behavior. A suggestion for this desired behavior is also included in this article. It is based on the impedance control approach in joint space. The proposed algorithm was implemented with the standard Stäubli RX90B industrial robot.     

Pure reactive behavior learning using Case Based Reasoning for a vision based 4-legged robot

A traditional problem in robotics is adaptation of developed algorithms to different platforms and sensors, as each of them has its specifics and associated errors. Hierarchical control architectures deal with the problem through division of the system into layers, where deliberative processing is performed at high level and low level layers are in charge of dealing with reactive behaviors and adaptation to platform and sensor hardware. Specifically, approaches based on the Emergent Behavior Theory rely on building high level behaviors by combining simpler ones that provide intuitive reactive responses to sensory instance. This combination is controlled by higher layers in order to obtain more complex behaviors. Unfortunately, low level behaviors might be difficult to develop, specially when dealing with legged robots and sensors like video cameras, where resulting motion is heavily influenced by the robot kinematics and dynamics and sensory input is affected by external conditions, transformations, distortions, noise and motion itself (e.g. the camera bouncing problem).In this paper, we propose a new learning based method to solve most of these problems. It basically consists of creating a reactive behavior by supervisedly driving a robot for a time. During that time, its visual input is reactively associated to commands sent to the robot through a Case Based Reasoning (CBR) behavior builder. Thus, the robot learns what the person would do in its situation to achieve a certain goal. This approach has two advantages. First, humans are particularly good at adapting and taking into account the specifics of a given mobile after some use. Thus, kinematics and dynamics are absorbed into the casebase along with how the person thinks they should be dealt with by that particular robot. Similarly, commands are associated to the input sensor as is, so systematic errors in sensors and motors are also implicitly learnt in the casebase (camera bouncing, distorsions, noise …). Also, different reactive strategies to reach a simple goal can be programmed into the robot by showing, rather than by coding. This is particularly useful because some reactive behaviors are ill-fitted to equations. Naturally, CBR allows online adaptation to potential changes after supervised training, so the system is able to learn by itself when working autonomously too.The proposed system has been successfully tested in a 4-legged Aibo robot in a controlled environment. To prove that it is adequate to create low level layers for hybrid architectures, two different CBR reactive behaviors have been tested and combined into an emergent one. A deliberative layer could be used to extent the system to more complex environments.     

Learning to Walk by Imitation in Low-Dimensional Subspaces

In this paper, we provide the first demonstration that a humanoid robot can learn to walk directly by imitating a human gait obtained from motion capture (mocap) data without any prior information of its dynamics model. Programming a humanoid robot to perform an action (such as walking) that takes into account the robot's complex dynamics is a challenging problem. Traditional approaches typically require highly accurate prior knowledge of the robot's dynamics and environment in order to devise complex (and often brittle) control algorithms for generating a stable dynamic motion. Training using human mocap is an intuitive and flexible approach to programming a robot, but direct usage of mocap data usually results in dynamically unstable motion. Furthermore, optimization using high-dimensional mocap data in the humanoid full-body joint space is typically intractable. We propose a new approach to tractable imitation-based learning in humanoids without a robot's dynamic model. We represent kinematic information from human mocap in a low-dimensional subspace and map motor commands in this low-dimensional space to sensory feedback to learn a predictive dynamic model. This model is used within an optimization framework to estimate optimal motor commands that satisfy the initial kinematic constraints as best as possible while generating dynamically stable motion. We demonstrate the viability of our approach by providing examples of dynamically stable walking learned from mocap data using both a simulator and a real humanoid robot.     

Failure of motor learning for large initial errors

For certain complex motor tasks, humans may experience the frustration of a lack of improvement despite repeated practice. We investigate a computational basis for failure of motor learning when there is no prior information about the system to be controlled and when it is not practical to perform a thorough random exploration of the set of possible commands. In this case, if the desired movement has never yet been performed, then it may not be possible to learn the correct motor commands since there will be no appropriate training examples. We derive the mathematical basis for this phenomenon when the controller can be modeled as a linear combination of nonlinear basis functions trained using a gradient descent learning rule on the observed commands and their results. We show that there are two failure modes for which continued training examples will never lead to improvement in performance. We suggest that this may provide a model for the lack of improvement in human skills that can occur despite repeated practice of a complex task.     

Learning model for coupled neural oscillators.

Neurophysiological experiments have shown that many motor commands in living systems are generated by coupled neural oscillators. To coordinate the oscillators and achieve a desired phase relation with desired frequency, the intrinsic frequencies of component oscillators and coupling strengths between them must be chosen appropriately. In this paper we propose learning models for coupled neural oscillators to acquire the desired intrinsic frequencies and coupling weights based on the instruction of the desired phase pattern or an evaluation function. The abilities of the learning rules were examined by computer simulations including adaptive control of the hopping height of a hopping robot. The proposed learning rule takes a simple form like a Hebbian rule. Studies on such learning models for neural oscillators will aid in the understanding of the learning mechanism of motor commands in living bodies.     

Learning of a controller for non-recurring fast movements

In this paper a learning method is described which enables a conventional industrial robot to accurately execute the teach-in path in the presence of dynamical effects and high speed. After training the system is capable of generating positional commands that in combination with the standard robot controller lead the robot along the desired trajectory. The mean path deviations are reduced to a factor of 20 for our test configuration. For low speed motion the learned controllers' accuracy is in the range of the resolution of the positional encoders. The learned controller does not depend on specific trajectories. It acts as a general controller that can be used for non-recurring tasks as well as for sensor-based planned paths. For repetitive control tasks accuracy can be even increased. Such improvements are caused by a three level structure estimating a simple process model, optimal a posteriori commands, and a suitable feedforward controller, the latter including neural networks for the representation of nonlinear behaviour. The learning system is demonstrated in experiments with a Manutec R2 industrial robot. After training with only two sample trajectories the learned control system is applied to other totally different paths which are executed with high precision as well.     

Simultaneous learning of perception and action in mobile robots

One of the main problems of robots is the lack of adaptability and the need for adjustment every time the robot changes its working place. To solve this, we propose a learning approach for mobile robots using a reinforcement-based strategy and a dynamic sensor-state mapping. This strategy, practically parameterless, minimises the adjustments needed when the robot operates in a different environment or performs a different task.Our system will simultaneously learn the state space and the action to execute on each state. The learning algorithm will attempt to maximise the time before a robot failure in order to obtain a control policy suited to the desired behaviour, thus providing a more interpretable learning process. The state representation will be created dynamically, starting with an empty state space and adding new states as the robot finds new situations that has not seen before. A dynamic creation of the state representation will avoid the classic, error-prone and cyclic process of designing and testing an ad hoc representation. We performed an exhaustive study of our approach, comparing it with other classic strategies. Unexpectedly, learning both perception and action does not increase the learning time.     

Inferring robot goals from violations of semantic knowledge

A growing body of literature shows that endowing a mobile robot with semantic knowledge and with the ability to reason from this knowledge can greatly increase its capabilities. In this paper, we present a novel use of semantic knowledge, to encode information about how things should be, i.e. norms, and to enable the robot to infer deviations from these norms in order to generate goals to correct these deviations. For instance, if a robot has semantic knowledge that perishable items must be kept in a refrigerator, and it observes a bottle of milk on a table, this robot will generate the goal to bring that bottle into a refrigerator. The key move is to properly encode norms in an ontology so that each norm violation results in a detectable inconsistency. A goal is then generated to bring the world back in a consistent state, and a planner is used to transform this goal into actions. Our approach provides a mobile robot with a limited form of goal autonomy: the ability to derive its own goals to pursue generic aims. We illustrate our approach in a full mobile robot system that integrates a semantic map, a knowledge representation and reasoning system, a task planner, and standard perception and navigation routines.     

Sensing through body dynamics

It has been shown that sensory morphology and sensory–motor coordination enhance the capabilities of sensing in robotic systems. The tasks of categorization and category learning, for example, can be significantly simplified by exploiting the morphological constraints, sensory–motor couplings and the interaction with the environment. This paper argues that, in the context of sensory–motor control, it is essential to consider body dynamics derived from morphological properties and the interaction with the environment in order to gain additional insight into the underlying mechanisms of sensory–motor coordination, and more generally the nature of perception. A locomotion model of a four-legged robot is used for the case studies in both simulation and real world. The locomotion model demonstrates how attractor states derived from body dynamics influence the sensory information, which can then be used for the recognition of stable behavioral patterns and of physical properties in the environment. A comprehensive analysis of behavior and sensory information leads to a deeper understanding of the underlying mechanisms by which body dynamics can be exploited for category learning of autonomous robotic systems.     

Recurrent cerebellar loops simplify adaptive control of redundant and nonlinear motor systems

We have described elsewhere an adaptive filter model of cerebellar learning in which the cerebellar microcircuit acts to decorrelate motor commands from their sensory consequences (Dean, Porrill, & Stone, 2002). Learning stability required the cerebellar microcircuit to be embedded in a recurrent loop, and this has been shown to lead to a simple and modular adaptive control architecture when applied to the linearized 3D vestibular ocular reflex (Porrill, Dean, & Stone, 2004). Here we investigate the properties of recurrent loop connectivity in the case of redundant and nonlinear motor systems and illustrate them using the example of kinematic control of a simulated two-joint robot arm. We demonstrate that (1) the learning rule does not require unavailable motor error signals or complex neural reference structures to estimate such signals (i.e., it solves the motor error problem) and (2) control of redundant systems is not subject to the nonconvexity problem in which incorrect average motor commands are learned for end-effector positions that can be accessed in more than one arm configuration. These properties suggest a central functional role for the closed cerebellar loops, which have been shown to be ubiquitous in motor systems (e.g., Kelly & Strick, 2003).     

State space models of remote manipulation tasks

A state variable formulation of the remote manipulation problem is presented, applicable to human-supervised or autonomous computer-manipulators. A discrete state vector, containing position variables for the manipulator and relevant objects, spans a quantized state space comprising many static configurations of objects and hand. A manipulation task is a desired new state. State transitions are assigned costs and are accomplished by commands: hand motions plus grasp, release, push, twist, etc. In control theory terms the problem is to find the cheapest control history (if any) from present to desired state. A method similar to dynamic programming is used to determine the optimal history. The system is capable of obstacle avoidance, grasp rendezvous, incorporation of new sensor data, remembering results of previous tasks, and so on.