A Control Architecture for Dynamically Stable Gaits of Small Size Humanoid Robots

A CONTROL ARCHITECTURE FOR DYNAMICALLY STABLE GAITS OF SMALL SIZE HUMANOID ROBOTS Andrea Manni ¤;1, Angelo di Noi ¤ and Giovanni Indiveri ¤ ¤ Dipartimento di Ingegneria dell'Innovazione, Universit`a di Lecce, via per Monteroni, 73100 Lecce, Italy, Fax: +39 0832 297279, email:fandrea.manni, giovanni.indiveri, [email protected] Abstract: From the 1970's biped robots have had a large attention from the robotic research community. Yet the issue of controlling dynamically stable walking for arbitrary biped robots is still open. We propose a simple control architecture based on the use of the FRI (Foot Rotation Indicator) point and the support polygon. The major advantage of the proposed architecture is that motion planning (and eventually sensor based re-planning (slower feedback loop)) is limited to the leg joints whereas the trunk and arm degrees of freedom are controlled in closed loop (faster feedback loop) to achieve overall dynamic stability. Such architecture allows to decouple the problem of dynamic stable walking in the two relatively simpler problems of gait generation and robot stabilization. This architecture is particularly suited for small size robots having limited onboard computational power and limited sensor suits. The e®ectiveness of the proposed method has been validated through Matlabr simulations and experimental tests performed on a Robovie-MS platform. Copyright °c 2006 IFAC Keywords: control architecture, dynamically stable gait, foot rotation indicator, support polygon. 1. INTRODUCTION over twenty actuated degrees of freedom and gen- erally they carry some microcontroller electronics Humanoid robots are enjoying increasing popular- board for the low level control, i.e. to generate ity as their anthropomorphic body allows the in- target signals for the actuators. Higher level con- vestigation of human-like motion and multimodal trol loops need by far more computational power communication. Currently, examples of advanced and are usually implemented either on industrial humanoid robots include Asimo (Honda, Inc) or controllers as, by example, PC104 or on handheld Qrio (Sony, Global), whereas simpler designs in- computers (Behnke et al., July 2005a)(Behnke et clude Vstone (Vstone, Co. Ltd), Kondo (Kagaku, al., May 2005b), such as Pocket PC and alike. The Co. Ltd) or RoboSapien (Wowwee, Robosapien), communication link between low and higher level which has been developed for the toy market. control loops is most often of serial RS232 kind. Small humanoid robots can have from a few to The actuators are usually low power servo motors from the radio control (RC) models market. 1 Corresponding author Fig. 1. Robovie-MS Fig. 2. De¯nition of the support polygon (single Biped locomotion is one of the most important (a) and double (b) support phases) issues to be faced: the basic characteristics of all biped locomotion systems are (Vukobratovi¶cand joint trajectories for dynamic walking is an im- Borovac, 2004): portant research area: several methods have been presented in the literature. Some of these are (1) the possibility of rotation of the overall sys- based on the inverted pendulum model for the tem about one of the feet edges caused by biped legs (Tsuji and Ohnishi, 2002), (Goswami strong disturbances; et al., 1997). Other more complicated techniques (2) gait repeatability; take directly into account dynamic stability in- (3) regular interchangeability of single and dou- dicators as the zero moment point (ZMP) (Zhou ble support phases. et al., 2004) or the foot rotation indicator (FRI) In this paper, we propose a control architec- (Ho®man et al., 2004). We consider a control ture for the motion control of a humanoid robot architecture based on the FRI (Foot rotation In- that allows to decouple the gait generation issue dicator) (Goswami, 1999), which is a point on and the overall dynamic stability of the system. the foot/ground contact surface where the net The analysis of dynamic stability is addressed on ground reaction force would have to act to keep the basis of the Foot Rotation Indicator (FRI) the foot stationary. To ensure the absence of foot (Goswami, 1999). The remainder of the paper is rotations around any axis laying in the ground organized as follows: the used robot is described in plane, the FRI point must remain within the con- the section 2, the proposed architecture in section vex hull of the foot support area. The proposed 3. Implementation issue are discussed in section 4. control architecture is shown in ¯gure 3. The basic Simulation and experimental results are presented idea, is that the leg joints only are considered for in section 5 and, ¯nally, conclusions are brieﬂy locomotion planning while the upper body and discussed in section 6. arm joints are used for dynamic stabilization. The aim is to design an architecture that allows to decouple the gait generation and dynamic stabilization problems. In essence, this architecture is 2. ROBOT DESCRIPTION inspired by classical task based control architec- tures (Sciavicco and Siciliano, 2000) of industrial The considered robot, shown in ¯gure 1, is the robots that allow to design separate control laws Robovie-MS, a small humanoid robot kit made for concurrent, but di®erent tasks. As for the gait by Vstone (Vstone, Co. Ltd). The robot has 17 generation, basically this will be commanded to degrees of freedom (DOFs): 5 in each leg, 3 in the leg joints based on an o® line (or "loose" feed- each arm and one in the head. It is 28 cm tall back) planning phase. Any of the standard gait and has a total weight of about 860g. It has planning approaches described in the literature one 2 axis acceleration sensor and 17 joint angle may be considered, eventually including obstacle sensors. The servos control board is composed avoidance tasks as suggested in ¯gure 3. by an H8 CPU at 20 MHz, a 56KByte FLASH- ROM memory, a 4KByte RAM and a 128KByte With reference to ¯gure 3, the gait generator is a External-EEPROM. planner for the leg joints only generating either leg joint torques (in case of a dynamic planner) or leg joint reference velocities (in case of a kinematics 3. CONTROL ARCHITECTURE planner). In either case the gait generator output is used to de¯ne the leg joint commands. As In this section we present the control architecture pictorially represented in ¯gure 3, such planner proposed to obtain a dynamically stable gait for may use joint information to perform obstacle the biped robot. The issue of planning desired avoidance planning or re-planning. As for the Fig. 3. Control architecture. dynamic stability control, the direct kinematics be compared to (Khatib et al., 2004) with the model will be used to compute the velocity and di®erence that in (Khatib et al., 2004) the task position of the center of the support polygon as a division is implemented at an algorithmic level, function of the joint values. The support polygon while in the present case at a control architecture can be de¯ned as the contact area between the level. humanoid robot and the ground; therefore in the single support phase, it is given by the sole in contact with the ground (seen ¯gure 2(a)), while 4. IMPLEMENTATION ISSUES in the double support phase, it is given by the convex hull of contact points between the soles The dynamic stabilization feedback control loop and the ground (seen ¯gure 2(b)). described in section 3 and in ¯gure 3 can be de- The dynamic stabilization controller will have signed based upon a Lyapunov technique. Want- as input the vector di®erence of the position of ing the FRI point to converge on a target point r t a target point inside the support polygon with within the support polygon, a quadratic Lyapunov the position of the FRI, and its aim will be to candidate function may be de¯ned as: drive this error to zero by acting on the upper body degrees of freedom. Indeed if FRI is in the 1 V = (r ¡ r )T R (r ¡ r ) (2) support polygon, we are sure that the robot's 2 t F RI t F RI motion is dynamically stable. It should be noticed where R will be a symmetric positive de¯ned that according to its de¯nition (Goswami, 1999), matrix, and r and r are the positions of the FRI tends to the ground projection of the F RI t the FRI and of a target point inside the support center of mass (GCoM, in the sequel) as the joint polygon respectively. The time derivative of V will accelerations tend to zero. Namely indicating with be given by: r F RI and r GCoM the position of the FRI and of the ground projection of the center of mass _ T respectively, the following holds: V = (_r t ¡ r_ F RI ) R (r t ¡ r F RI ) = (3) ³ ´T ³ ´ _ ± := r F RI ¡ r GCoM =) lim ± = 0 (1) = ¡ r_ GCoM ¡ r_ t + ± R r t ¡ r GCoM ¡ ± ai;!_ i!0 being ± de¯ned in equation (1). Calling q ; q being a and! _ the linear and angular acceler- L UB i i the legs and upper body joint variables and J (q), ations of each link. Notice that ± is a continu- L J (q) the legs and upper body Jacobian matri- ous function of the link accelerations and that if UB ces such that jajj < g 8 j, then k±k is upper bounded. Decoupling the gait planning and dynamic sta- r_ GCoM = JL(q)_qL + JUB(q)_qUB; (4) bilization tasks is particularly important for small size robots that have limited computational equation (3) suggests to compute the reference power. In order for such decoupling to be e®ec- value of the upper joint velocities as tive, the cycle time of the dynamic stabilization h i controller needs to suitably smaller than the gait y q_UBd = J R (r ¡ r ) ¡ JLq_L +r _ (5) period.

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