THE DYNAMIC APPROACH TO ANTHROPOMORPHIC ROBOTICS Axel Steinhage ∗
∗
Institut f¨ ur Neuroinformatik, Ruhr-Universit¨ at Bochum, 44780 Bochum, Germany
[email protected] www.neuroinformatik.ruhr-uni-bochum.de/ini/PEOPLE/axel/top.html
Abstract: The ultimate task for today’s autonomous robots is the problem of man-machine interaction. This task sets high standards with respect to flexibility, stability, safety and efficiency of the generated robot behavior. We present a control architecture which is capable of both: the generation and organization of stable elementary behaviors based on low-level sensor information and the implementation of cognitive concepts like memory, internal simulation and learning. Based on the so-called Dynamic Approach to Robotics our approach tries to mimic the basic working principles of nervous systems of biological organisms. Pushing the parallels to biology even further we restrict ourselves to so-called anthropomorphic robots which have similarities with the human concerning the external body form and the sensor equipment. Copyright Controlo 2000 Keywords: Dynamical Systems, Anthropomorphy, Robotics, Man-Machine Interaction, Cognition
1. INTRODUCTION For several decades already robots have proven their feasibility in industrial production processes. Countless special purpose machines efficiently perform monotonous actions in scenarios that are designed specifically for the robots and the task they have to fulfill. To generate the desired behavior within these situations classical control theory extended by newer concepts for sensor processing, sensor fusion and operator driven optimization of the elementary behaviors has proven to be very successful. In parallel to this development, particularly during the last decade, a growing interest arose in the field of robotics research that is occupied with the behavior of so-called autonomous robots in dynamic environments. Although most experimental setups within this research rather deal with toy problems than with real world applications (e.g. the soccer playing robots (Kitano et
al. 1995), pallet collecting robots (Mataric 1997) etc) it already turned out that neither classical control theory nor the symbolic approach of classical artificial intelligence (AI) is appropriate for the behavior generation of these robots. While the symbolic approach of AI has great success in purely cognitive tasks like chess playing, it lacks the seamless coupling with the continuously varying parameters of the real world that is required to generate stable behavior for an autonomous system. Classical control theory, however, fails in providing the system with the necessary flexibility to generate multiple different stable behaviors depending on the dynamic change of the environment. Although there are architectures like the so-called Hybrid Systems (Grossman 1993) which try to exploit the advantages of AI and control theory by coupling discrete algorithms with continuous control dynamics, these approaches seem not particularly successful in the domain of au-
tonomous robotics. The reason for this may be the interface between these two inherently different methods which causes potential instabilities (see (Steinhage 1998) page 104 for a criticism of Hybrid Systems in robotics).
relatively homogenous architecture. Therefore, it seems to be justified to search for a unified control architecture for artificial systems too. This is the task that we are concerned with. Our work is guided by two insights:
A number of new control architectures have been developed (e.g. the Behavior Based Approach (Brooks 1991), the Dynamic Approach (Sch¨ oner et al., 1995) or the Dual Dynamics Approach (Jaeger & Christaller 1997)) which account for the problem of autonomous robotics by putting the focus on the so-called elementary behaviors a complex action consists of. These approaches are based on ideas that were first formulated by Braitenberg (Braitenberg 1984) and have been very successful by abstaining from any kind of representation of the external world or the agent therein. The elementary behaviors are generated by relying on low-level sensor information only. In this respect the behavior based approaches are much closer to the domain of control theory than to the field of AI which inherently relies on internal models or representations of the world. However, although remarkably complex behavior has been generated by behavior based systems 1 , there are tasks that require a certain degree of cognition and internal representation. This situation is given, for instance, when the current sensor information is not sufficient to generate appropriate behavior and a memory of previously encountered situations or even an internal simulation of the situation’s development in the future is required.
1) The environment and all behaving systems therein are physical, high dimensional dynamical systems that are tightly coupled by the dynamic interactions instantiated by the functions perception and action. From this point of view dynamical systems theory seems to be the mathematical tool of choice for the design of a behavior generating architecture. We therefore build our architecture based on the so-called Dynamic Approach to Robotics (originally formulated by Sch¨ oner (1995) ) which heavily relies on the mathematics of dynamical systems. We extend this approach by new cognitive components while keeping the basic theory unchanged.
The ultimate task in which cognition and representation for autonomous robots become relevant is the problem of man-machine interaction e.g. in service-robotics: here the robot is not totally independent but must take into account the behavior of the human it interacts with. The robot must be able to react flexibly and in real time to the permanent variation of the environment brought about by its own behavior and by the behavior of the human partner. The task is aggravated if an additional requirement for the system is to learn from errors or from the human’s actions. Furthermore, man-machine interaction puts a strong emphasis on the stability and the safety of the robot as the risk of endangering the human partner by instable behavior must be avoided under all circumstances. The question is, what kind of control architecture is needed to generate and organize robot behavior under these tight conditions ? Interestingly, the nervous system of biological organisms solves all the problems from low level sensor processing to high level cognition using a 1
see e.g. (Steinhage 1998), in which a system is described which organizes more than ten different elementary behaviors
2) By evolution the body structure and the nervous system of biological organisms are highly optimized for their specific environment. For the problem of man-machine interaction it therefore seems natural to build the body structure and the behavior generating control architecture similar to the human role model. This latter aspect runs under the keyword anthropomorphy. In the following we will at first present the anthropomorphic robots Arnold and Cora that serve as experimental platforms for our approach. Then we will briefly describe the basic principles of the Dynamic Approach to Robotics and the extensions that we added to it. In a number of examples we will show practical robotic implementations which demonstrate the capabilities of the approach. Finally, we will present new ideas for cognitive processes based on dynamical systems that are inspired by the knowledge that researchers have in the meantime about the working principles of cortex areas. Limited space does not allow a detailed description of the mathematical concepts and methods. We would like to direct the interested reader towards the list of publications that can be downloaded from our web-site. 2. THE ANTHROPOMORPHIC ROBOTS ARNOLD AND CORA 2.1 Arnold Arnold (see Fig. 1) has been designed as a prototype of a general purpose service robot for indoor environments. The platform is a modified TRC Labmate (80x80 cm) carrying a pyramidal body of about 145 cm height. At a height of about 1 m a seven degree of freedom (DoF) Amtec arm is mounted the design of which is anthropomorphic: like with the human arm Arnold can grasp
invented by Sch¨ oner (1995), is to parameterize a behavior by a scalar or vector valued behavioral variable x ∈ RN . For example, the locomotion of Arnold is expressed by the vector xloc = (nloc , v, φ) of the robot’s forward velocity v, its heading direction φ and a variable nloc ∈ [0, 1] which indicates to which degree the locomotion behavior is active. the behavior is generated by assigning values to x which are used by the motor system of the robot to drive the wheels. Now comes the main trick: we design the differential equation of a dynamical system ˙ τ u(x, t) = F (u(x, t), s(x, t)) Fig. 1. The anthropomorphic mobile robot Arnold (left) and the anthropomorphic assembly robot Cora (right) while exploiting the redundant seventh DoF for obstacle avoidance. The arm is controlled via a serial CAN bus. Above the arm a stereo camera system with two high-resolution fovea color cameras and two wide-angle greylevel cameras is located. Their functionality mimics the foveal and peripheral viewing capabilities of the human vision system. The camera head further incorporates a stereo microphone system. Three Pentium PC’s connected via Fast Ethernet and running under the realtime operating system QNX are integrated on Arnold. A detailed description of Arnold’s hardware and software design can be found in (Bergener et al., 1999).
the solution of which evolved in time generates the desired behavior. In (1), u(x, t) is a function ˙ of the behavioral variable, t is the time, u(x, t) = ∂u(x,t) is the derivative of u with respect to ∂t time, s(x, t) is a vector of parameters, that we also call input and τ is the time scale of the dynamics. For the function u(x, t) our approach offers two choices so far: In the first case, u is the excitation of a so-called neural field defined over the behavioral variable x. The activity of the field represents to which extent the corresponding value of the behavioral variable is specified. This mathematical concept captures many aspects of biological information processing. We will give examples later. In the second, so-called instantiated case, we can formally set u(x, t) ≡ x(t) such that the dynamics (1) simplifies to
2.2 Cora Cora (=Cooperative Robot Assistant, see Fig. 1) is our very new creation: an anthropomorphic seven DoF-arm similar to the one of Arnold connected to a one DoF-trunk which is fixed on a table. Cora was designed to investigate aspects of man-machine interaction in assembly tasks. The focus of our research is put on the perception, representation and analysis of the scene which consists of the objects to assemble, the robot itself and the human counterpart who is sitting at the table across Cora. To capture the relevant aspects of the scene, Cora is equipped with a two DoF vision head and microphones similar to the ones of Arnold. In addition we will provide parts of Cora’s arm with artificial skin to add a haptic sensor. The computational equipment consists of five Pentium PC’s running under QNX. 3. BASIC PRINCIPLES OF THE APPROACH
(1)
˙ τ x(t) = F (x(t), s(x, t)) .
(2)
The concrete form of F depends on the behavior to generate and is subject to the designer’s skill. However, our approach contains some general rules which facilitate the design process and help to keep the dynamics stable: First, the dynamics must be designed such that desired values xS of the behavioral variable specify stable states (attractors) and undesired values xU specify unstable states (repellers) of the dynamics (2). This requirement ensures that the dynamics will keep the behavioral variable near desired values even when noise or perturbations act on the system. The values xS of the stable states are specified by the system’s sensors by means of the input vector s(x, t). For example, for target acquisition the robot’s sensors measure the angular position φtar (t) = sloc (t) of a target. Then, a dynamics for the φ-coordinate of the behavioral variable xloc ˙ = φtar (t) − φ(t). This dynamics could be: τloc φ(t) has a stable fixed point at φ = φtar 2 and there-
3.1 Behavioral variables and Dynamical Systems For φ = φtar the variation in time φ˙ = φtar − φ vanishes ∂ φ˙ and as the slope ∂φ |φ=φtar = −1 of the phaseplot in the fixed point is negative, this fixed point is stable. 2
The fundamental idea of our approach, which is based on the Dynamic Approach to Robotics
fore the behavioral variable (and hence the robot’s heading) will relax to this value. Multiple desired behaviors can be accounted for by designing a dynamics with multiple stable states such that phase changes or bifurcations of the dynamics result in changes of the behavior. Undesired states, such as the direction towards obstacles, can be accounted for by setting unstable fixed points (repellers) for these values (Steinhage & Sch¨ oner 1997). This principle has been used successfully in many robotic implementations (see e.g. (Bicho & Sch¨ oner 1997a), (Bicho & Sch¨ oner 1997b)). For Arnold we exploit instantiated dynamics in many ways. One example is the door-passingbehavior: With its stereo-vision system Arnold can detect and identify doors and their distances and orientations relative to the robot (Steinhage & Bergener 1998). Once the right door to pass through is identified a smooth trajectory can be generated by approaching a location D in front of the door from far distances rD by driving in direction ϕD and then turning into a perpendicular orientation ϕT towards the threshold of the door at near distances (see Fig. 2). These two 111111111 000000000 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111
multiple parts can be fused in a simple dynamics by a summation of their corresponding attractors.
3.2 Time Scale Relations The second rule of our approach states that the time scale on which the input s(x, t) changes must be much slower than the time scale τ of the dynamics (see (Steinhage & Sch¨ oner 1997) for a discussion). This is obvious for the example of target acquisition: if the angular position of the target changes faster than the time the dynamics needs to relax to the stable state the system does not work properly anymore. However, as the choice of the time scale τ of the dynamics is up to the designer, the time scale requirement can always be met. This so-called separation of time scales also allows to couple multiple dynamics in the way that one slow dynamics j specifies the parameters si (xi , t) of a second, faster dynamics i. For instance we have realized very smooth natu-
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Fig. 3. Grasping objects from a human’s hand.
Fig. 2. Door passing behavior: After approaching a location D in front of the door, the robot turns perpendicular to the door an passes through. parts of the overall goal to pass the door can be expressed by two terms on the right hand side of the behavior generating dynamics of the type (2): τϕ ϕ˙ = n1 sin(ϕD − ϕ) + n2 sin(2ϕD − ϕT − ϕ) n1 = 1 − e
2 −rD /δ 2
,
n2 = e
2 −rD /δ 2
(3)
The second term can be neglected for large distances rD ≫ δ = const where n2 ≃ 0, while the first term can be neglected for small distances rD ≪ δ for which the exponential function is ≃ 1. If the first term is active, the robot dives into the direction of the attractor ϕ = ϕD , if the second term is active, it drives towards the attractor ϕ = 2ϕD −ϕT which is the direction perpendicular to the door. This shows how tasks consisting of
rally looking behavior by letting the dynamics for the head direction run on a faster time scale than the grasping dynamics which, in turn, runs faster than the platform movement dynamics. Arnold is able to take objects from the hands of humans by tracking the objects visually on a fast time scale, grasping for them on a slower time scale and following the person with the platform on the slowest time scale (see Fig. 3).
3.3 Behavioral Organization Following the principles of the Dynamic Approach to Robotics we have implemented many elementary behaviors such as grasping and handing over (Bergener & Dahm 1997), navigation (Bergener et al., 1999), door passing (Steinhage & Bergener 1998), acoustical guidance (Menzner & Steinhage 1999) etc. For the organization of all the elementary behaviors and the generation of appropriate behavioral sequences we have developed a dynamic architecture which controls the
presence of attractor components i in the control dynamics by means of the activity parameters ni in equations of the type (3) every elementary behavior that acts on the same behavioral variable is represented by a contribution the sum of which adds up to the control dynamics of that behavioral variable: τx =
N X
n2i fi (x, si )
(4)
i=1
The contributions fi can be linear or nonlinear attractors. The activities ni are controlled by a dynamics which has stable states at ni = 0 or ni = ±1 depending on a parameter αi . n˙ i = αi ni − |αi |n3i
(5)
αi = g(s, n, L, A)
(6)
For negative values αi < 0 equation (5) has a stable fixed point at ni = 0 which means behavior i is not active. Going to positive values αi > 0 a bifurcation is induced on the dynamics and the state ni = 0 becomes unstable while the stable states ni = ±1 arise that correspond to an active behavior i. An active elementary behavior contributes with an attractor term to the control dynamics (4) of the behavioral variable by n2i = 1 and therefore influences the behavior of the robot. The parameters αi depend on the sensor inputs s, the activity pattern n = (n1 , n2 , . . . , nN ) of elementary behaviors, on the so-called logics-matrix L = {Li,j } and on the so-called activity-matrix A = {Ai,j }. The matrix L encodes fixed logical dependencies between the elementary behaviors: if, for instance, two behaviors i and j cannot coexist (like e.g. driving back and driving forth) this is coded by a fixed entry Li,j = 3. If a behavior i requires the simultaneous activity of behavior j (e.g. “driving” requires “obstacle avoidance”) we encode this by Li,j = 1. If a behavior i requires the activity of any of the behaviors j, k, l, . . . the entries Li,j = Li,k = Li,l = . . . = 2 are set. Logical independence between two behaviors i and j is encoded by Li,j = 0. Through the activity matrix A a behavior j can switch on (Ai,j = 1) or off (Ai,j = −1) a behavior i. The whole system for behavioral organization can be designed by only setting the matrices L and A which couple all dynamics (5) to one multidimensional nonlinear dynamics. We have implemented a so-called acoustical joystick for Arnold in this way: the navigation and pointing behaviors are controlled by speech commands that serve as the sensor input s for the behavioral organization. For the concrete form of the function g and a number of implementations we refer the reader to (Steinhage & Sch¨ oner 1998),
(Bergener & Steinhage 1998), (Menzner & Steinhage 1999) and (Menzner et al. 2000). 3.4 Learning We have extended the architecture for behavioral organization towards learning of behavioral sequences (Steinhage & Bergener 2000). This was done by modifying the sensor context s: an additional matrix V, the so-called voting matrix, codes the “motivation” of a behavior i to activate a behavior j. This motivation is high if, during an explorative or guided learning phase, behavior j turns out to produce the necessary sensor context for behavior i. If this is the case, behavior j must be activated before behavior i in a sequence. Expressing the final goal of the sequence by a specific behavior, the necessary steps to reach this state can be recursively generated autonomously by the system. This way of generating behavioral sequences is motivated by research on learning and behavioral organization in biology (Timberlake & Silva 1995). 3.5 Neural Fields In addition to instantiated dynamics the general formulation of (1) contains another type of dynamics: the so-called Neural Field (Amari 1977). For navigation we use a one dimensional Amaritype neural field with asymmetric homogeneous kernel for the forward direction φ of Arnold: τ u(φ, ˙ t) = −u(φ, t) + s(φ, t) − h Z∞ + ω(φ − φ′ )f (u(φ′ , t))dφ′
(7)
−∞
˜ ˜ ∂ωs (φ) ∂ωs (φ) + n2r (8) ∂ φ˜ ∂ φ˜ 1 f (u) = −cu , φ˜ = φ − φ′ (9) e +1
˜ = ωs (φ) ˜ − n2 ω(φ) l with and
˜2 φ
˜ = ke− 2σ2 − H0 ωs (φ)
(10)
Herein ωs is a symmetric function of Gaussian type (k, σ and H0 are positive constants) and f (u) is a sigmoidal function (c is a positive constant). The functionality of the neural field can be understood best with the help of Fig. 4: The input s(φ, t) is the sum of a positive component specified by the direction of potential targets Ti (dotted line) and a negative component specified by the direction of potential obstacles Oi (dashdotted line). For nr = nl = 0 the so-called interaction kernel (8) is symmetric and the dynamics (7) relaxes to a stable peak solution (solid line) the maximum of which specifies the direction for the robot’s forward movement. This peak
ωs−∂ωs/∂φ
the information processing of cortical areas on a functional level. Taking into account that the brain has a relatively uniform and homogenous structure (at least compared to its tremendous functional flexibility), it seems reasonable to believe that neural fields could be the first step towards a general mathematical theory of cognition. We have started to go in that direction with a new architecture that we will now briefly present.
ωs+∂ωs/∂φ T2
u(φ)
T1
0 h O2 O1 0
φ
A practical example in which a certain degree of cognition is necessary is the problem of scene representation and scene interpretation. For our
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Fig. 4. Neural field for navigation: the current direction is indicated by the monostable peaksolution (solid line) which can be shifted right or left by an asymmetric kernel ω. makes a compromise between obstacle-avoidance and target-acquisition (see also (Bergener et al., 1999) for decision making using neural fields). If either the elementary behavior “move left” (n2l = 1) or “move right” (n2r = 1) is activated by the corresponding keyword, the kernel becomes asymmetric in the corresponding direction. This is accomplished in (8) by adding to the kernel function its spatial derivative ± ∂ω ˜ . This asymme∂φ try makes the peak move with a constant velocity towards the corresponding direction until the kernel becomes symmetric again by de-activating the corresponding elementary behavior. A detailed mathematical analysis of this concept is contained in (Menzner et al. 2000). The main advantage of neural fields in this context is the possibility to fuse multiple behavioral requirements (obstacle avoidance, target acquisition, guided movement) within a single dynamics. For this reason we also use neural fields for the control of Arnold’s and Cora’s robot arms. In that case the requirements stem from obstacle avoidance, target acquisition, joint limits and haptic contacts by means of the artificial skin.
4. NEW IDEAS FOR REPRESENTATION, ASSOCIATION AND COGNITION In the previous sections we have described how dynamical systems can be applied to the problem of behavior generation, behavioral organization, learning of behavioral sequences and the intelligent fusion of multiple behavioral constraints. However, current research in neurobiology, neurophysiology and psychology suggests, that dynamical systems and neural fields are also well suited to qualitatively and quantitatively model cognitive processes (see e.g. (Jancke et al. 1999), (Giese 1999)). Neural fields can, for instance, describe
Fig. 5. A simulation of our robot Cora in an assembly scene. interactive robot Cora a scene consists of the objects to assemble, the human interaction partner and the robot itself. This scene is dynamic: the objects, the users hands and the robot manipulator may change their absolute locations and their geometric relations. The scene therefore consists of a continuous temporally ordered series of sensor inputs. For a seamless interaction with the human, Cora makes use of the following “information channels”: • vision: with the stereo camera system mounted on the pan-tilt unit Cora visually captures the current scene. The location of objects in the focus of view can be expressed by the coordinates pan, tilt and depths (p, t, d). By means of a number of advanced image processing algorithms that we have developed, Cora can detect and track the position of the user’s hands (hx , hy , hz ), the user’s face (fx , fy , fz ) and, most importantly, the users direction of gaze (γ1 , γ2 ). Furthermore, Cora can detect the color co of objects it fixates. By means of a number of computer vision algorithms, the size so and class Co of the observed objects can be determined. • audition: using a keyword recognizer in the way we already described, Cora accepts
spoken commands wi from a set of trained words. In this way, the user can also name objects by issuing a defining word while the robot fixates an object. Via a speaker Cora can also emit audio samples. This can be used, for instance, to ask for help from the user in ambiguous situations. • haptic: by means of the wrist force feedback sensor and the artificial skin that we will cover some elements k of the robot arm with, Cora can detect the normal direction and magnitude of force (Fk,x , Fk,y , Fk,z ) acting on these elements. • forward kinematics: using the forward kinematics, the robot always knows the position (ex , ey , ez ) of its own end-effector. • behavioral organization: we control the activity ni of Cora’s elementary behaviors by means of the architecture we already presented. Therefore, the set of variables {ni } represents the current behavioral state of the robot. The time series of the variables obtained by these channels together define the scene. The final task for Cora is to interprete the scene and to generate appropriate behavior in an interactive assembly task: the robot should learn from the behavior of the human so that it can autonomously repeat actions. Furthermore, Cora should detect when the user needs help and act accordingly. The robot should react on speech commands and gestures issued by the user and it should interprete the human’s gaze direction as the current focus of attention within the scene. As between two humans, the contextual information about the counterpart’s behavioral state should be transmitted by vision and audition. A first step towards this very ambitious goal is to represent the scene. We currently develop an architecture, in which every variable that belongs to the description of the scene, is the state variable of a one dimensional neural field of the type (7). The neural fields interact through a memory (see Fig. 6): all excitations uj (x, t) are permanently stored in and retrieved from an associative matrix memory. The output of the memory is fed back into the fields as weak part of the input sj (x, t). The state of the fields and the associative memory is a distributed representation of the scene and its recent history. The feedback of the fields’ activities through the memory acts as so-called preshape on the neural fields (Erlhagen & Sch¨ oner 1999): missing or ambiguous sensor input can be completed and disambiguated. Issuing the name of an object, for instance, can lead to a stabilization of peaks in the fields which represent the color or class of the object with that name. This is particularly useful when the current sensor input for that object is missing in a situation where the robot does not
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Neural Field Equation
.u(x,t) = -u(x,t) - h + s(x,t) + ω(x,x’) f (u(x’,t)) dx’ grasp Cylinder
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Fig. 6. Scene representation: all variables that represent the current scene are state variables of one-dimensional neural fields. These fields interact via an associative memory. look in the object’s direction. An other example is the selection of objects to grasp: the user’s gaze direction which can be interpreted as the focus of attention can disambiguate between multiple objects in question. Further research will deal with the question in how far this architecture can be used for internal simulation to plan and optimize behavior. However, the main problem that has to be solved for such a system of multiple coupled nonlinear dynamical systems is the mathematical proof of its stability. Especially the feedback of excitation into the fields through the associative memory requires a careful tuning of the parameters.
5. SUMMARY We have presented a unified approach to generate, organize and learn robot behavior. This approach is based on the Dynamic Approach to Robotics which we have extended by a number of new methods that are specifically useful in the domain of anthropomorphic robotics. By means of several implementations on our robot platform Arnold we have shown that the dynamic approach can be applied to the demanding problem of manmachine interaction. Inspired by findings from neurobiological research, we currently develop a neural field based architecture for cognition. We also presented our new anthropomorphic robot
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