Vertical motion control of a one legged hopping robot

Hopping movement is a desirable locomotion for a mobile robot to adapt on unknown surface and overcome the obstacles avoidance problem. The hopping locomotion is one of locomotion produced by legged robot. The legged type robot has difficult mechanism and complexity in control system. The hopping robot is designed to avoid the obstacles vertically. So, if the hopping robot takes too long time to reach the desired height, it will produced damages to the hopping robot physical. Therefore, the research on develop control strategies of one legged hopping robot is useful so that the developed control strategies can be used and extended to the multi-legged system. Central Pattern Generator (CPG) is a neural network that capable to generate continuous and rhythmic pattern. Since the hopping movement is a continuous and rhythmic jumping movement, it is synthesized that CPG neural network capable to generate hopping movement. Thus, the objectives of this research is to model the one legged hopping robot experimentally, to design a classic controller and integrate with CPG to compensate the steady-state error at each different height, and to optimize the parameters values of Central Pattern Generator (CPG) for the optimum rise time and steady-state error. A hopping peak height detector algorithm is designed to determine hopping peak height as feedback loop. The PI-CPG neural network parameters are optimized for each reference hopping height via simulation. The performance of optimized PI-CPG neural network is evaluated and compared with optimized PI and PID controller. The result shows that the optimized PI-CPG neural network controller produced better response which is 21.36 %, 24.20 %, and 44.13 % average rise time faster than PI-CPG, optimized PI, and optimized PID controller respectively. Moreover, the optimized PI-CPG controller more accurate in term of 4.91 % steady-state error compared to PI-CPG controller; 8.69 %, optimized PI controller; 6.03 %, and optimized PID controller 12.52 % average steady-state error for each reference hopping height. As a conclusion, the hopping height produced by the optimized PI-CPG neural network is more accurate and precise

The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates

We have built a 12DOF, passive-compliant legged, tailed biped actuated by four brushless DC motors. We anticipate that this machine will achieve varied modes of quasistatic and dynamic balance, enabling a broad range of locomotion tasks including sitting, standing, walking, hopping, running, turning, leaping, and more. Achieving this diversity of behavior with a single under-actuated body, requires a correspondingly diverse array of controllers, motivating our interest in compositional techniques that promote mixing and reuse of a relatively few base constituents to achieve a combinatorially growing array of available choices. Here we report on the development of one important example of such a behavioral programming method, the construction of a novel monopedal sagittal plane hopping gait through parallel composition of four decoupled 1DOF base controllers. For this example behavior, the legs are locked in phase and the body is fastened to a boom to restrict motion to the sagittal plane. The platform's locomotion is powered by the hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of template reference systems along with data from the physical platform suggesting these templates are anchored as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel composition of templates for tail-energized planar hopping," in 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015. v2: Used plain latex article, correct gap radius and specific force/torque number

Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control

This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angular momentum, taking as an addition output in the CLF-QP, is also stabilized in the jumping phase to prevent whole body rotation in the underactuated flight phase. The solution to the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping behaviors on bipedal robots with compliance. The framework presented in this paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 201

Extending The Lossy Spring-Loaded Inverted Pendulum Model with a Slider-Crank Mechanism

Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical systems resulted in newer models which are extended versions of original SLIP with viscous damping in the leg. However, such lossy models require an additional mechanism for pumping energy to the system to control the locomotion and to reach a limit-cycle. Some studies solved this problem by adding an actively controllable torque actuation at the hip joint and this actuation has been successively used in many robotic platforms, such as the popular RHex robot. However, hip torque actuation produces forces on the COM dominantly at forward direction with respect to ground, making height control challenging especially at slow speeds. The situation becomes more severe when the horizontal speed of the robot reaches zero, i.e. steady hoping without moving in horizontal direction, and the system reaches to singularity in which vertical degrees of freedom is completely lost. To this end, we propose an extension of the lossy SLIP model with a slider-crank mechanism, SLIP- SCM, that can generate a stable limit-cycle when the body is constrained to vertical direction. We propose an approximate analytical solution to the nonlinear system dynamics of SLIP- SCM model to characterize its behavior during the locomotion. Finally, we perform a fixed-point stability analysis on SLIP-SCM model using our approximate analytical solution and show that proposed model exhibits stable behavior in our range of interest.Comment: To appear in The 17th International Conference on Advanced Robotic

Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-down and mid-stance, and its damper auto-disengages during mid-stance and takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion