PaperlayerView exact revision on arXiv

Source-linked AI summary

The MIT Humanoid Robot: Design, Motion Planning, and Control For Acrobatic Behaviors

Matthew Chignoli, Donghyun Kim, Elijah Stanger-Jones, Sangbae Kim

arXiv:2104.09025v1cs.RO

TL;DR

Humanoid acrobatics require coordinated hardware, planning, and control because impulsive motions and landings impose demanding actuator and feedback requirements. The paper develops a humanoid, an actuator-aware kino-dynamic planner, and a dynamically consistent MPC-WBIC landing controller, validating actuators experimentally and in simulation. The resulting framework demonstrates back flips, front flips, and spinning jumps in realistic dynamics simulation.

  • Problem

    Humanoid acrobatic motions require systematic hardware, motion-planning, and control approaches, but prior demonstrations lacked documentation of their methodology and replication guidelines.

  • Method

    The paper combines custom proprioceptive actuators, an actuator-aware kino-dynamic planner, actuator-inclusive dynamics simulation, and dynamically consistent MPC-WBIC landing control.

  • Results

    The system demonstrates back flips, front flips, and spinning jumps in realistic dynamics simulation, with actuator outputs checked against experimentally validated torque-velocity limits.

  • Takeaways & Limitations

    The integrated design provides a practical system framework for simulating and preparing highly dynamic humanoid motions while accounting for actuator limits and landing feedback.

Abstract

from arXiv · show

Demonstrating acrobatic behavior of a humanoid robot such as flips and spinning jumps requires systematic approaches across hardware design, motion planning, and control. In this paper, we present a new humanoid robot design, an actuator-aware kino-dynamic motion planner, and a landing controller as part of a practical system design for highly dynamic motion control of the humanoid robot. To achieve the impulsive motions, we develop two new proprioceptive actuators and experimentally evaluate their performance using our custom-designed dynamometer. The actuator's torque, velocity, and power limits are reflected in our kino-dynamic motion planner by approximating the configuration-dependent reaction force limits and in our dynamics simulator by including actuator dynamics along with the robot's full-body dynamics. For the landing control, we effectively integrate model-predictive control and whole-body impulse control by connecting them in a dynamically consistent way to accomplish both the long-time horizon optimal control and high-bandwidth full-body dynamics-based feedback. Actuators' torque output over the entire motion are validated based on the velocity-torque model including battery voltage droop and back-EMF voltage. With the carefully designed hardware and control framework, we successfully demonstrate dynamic behaviors such as back flips, front flips, and spinning jumps in our realistic dynamics simulation.

I. INTRODUCTION

The paper addresses the lack of documented, reproducible approaches for humanoid acrobatics by unifying hardware design, motion planning, and landing control. It validates the system through actuator experiments and realistic simulations of flips, spins, and jumps.

  • Motivation: The paper targets highly dynamic humanoid motions that existing robot designs and control methods have not systematically documented or enabled.Prior work focused largely on minimally dynamic tasks, while hydraulic and compliant actuation introduce challenges for acrobatics.
  • Motion planning: Full-body trajectory optimization can exploit robot dynamics but suffers from local minima and long solve times, making manual trajectory design impractical.Reduced-order models are presented as a way to circumvent these planning difficulties.
  • Landing control: Stable landing requires long-horizon kinetic-energy dissipation while rapidly correcting errors from model mismatch and disturbances.The paper addresses this tension by combining model-predictive control with whole-body impulse control.
  • Contributions: The unified system combines a humanoid design, an actuator-aware kino-dynamic planner, and a hierarchical MPC-WBIC landing controller.The planner incorporates actuator limits, while the controller transfers MPC outputs to whole-body control.
  • Validation: Actuator performance is experimentally validated and incorporated into simulation to check that demonstrated motions are feasible on the assembled robot.The evaluation includes custom actuators and a dynamics simulation framework modeling actuator and robot dynamics.

II. SYSTEM OVERVIEW

The MIT Humanoid applies the MIT Cheetah design paradigm to combine powerful actuation, high-bandwidth force control, and impact mitigation for dynamic motions.

  • Design paradigm: The design uses torque-dense electric motors, high-bandwidth force control, and backdrivability to generate propulsion impulses and tolerate landing impacts.These principles were developed in previous MIT Cheetah robots and transferred to the humanoid design.

A. Robot Design

The MIT Humanoid is a compact robot whose mass is concentrated in the torso, shoulders, and hips and whose legs use five custom actuators each.

  • Physical configuration: The robot is approximately 0.7 m tall and weighs approximately 21 kg.Approximately 75.6% of its mass is in the torso, shoulder, and hip, 22.5% in the legs, and 1.9% in the arms.
  • Actuated joints: Each leg has five custom actuators for three hip joints, one knee joint, and one pitch-direction ankle joint.The knee, ankle, and elbow joints use belt gearing to provide higher torques.
  • Contact sensing: The robot’s foot contact timing is detected using wireless sensors attached to each heel and toe.There are four contact sensors in total.

B. Custom Actuator Design

The humanoid uses two custom high-torque-density motor modules, validated with a dynamometer and designed to meet the torque demands of impulsive motion.

  • Motor modules: The U12 and U10 modules adapt Mini-Cheetah actuator designs to meet the humanoid’s increased torque requirements.Their drivers were modified for the higher voltage and power levels needed by the robot.
  • Experimental validation: A custom dynamometer with a Futek TRS300 torque sensor measures actuator peak torque and torque constant for simulation modeling.Peak torque is identified as the critical capability for dynamic-motion feasibility.
  • Measured limits: 31 Nm is the approximate saturation point of the U10 module, while the U12 reaches its 68 Nm gearbox mechanical limit before saturation.These peak-torque results are reported from dynamometer testing.

C. Actuator and Battery Dynamic Model

The actuator and battery model combines measured motor parameters with torque-speed limits and voltage droop to estimate time-varying actuator capabilities. The framework also includes empirically verified motor behavior and planning/control context for dynamic motion.

  • Actuator model: Measured motor parameters are combined with inductance and resistance measurements to model the motors’ torque-speed curves.The model also includes estimates of damping and friction coefficients.
  • Speed and voltage limits: Back EMF limits q-axis current when stator voltage exceeds the available bus voltage at high speed, reducing torque capability.Field weakening can increase torque at reduced efficiency, but was unnecessary for the reported trajectories.
  • Model visualization: Figure 4 compares current with torque and shows empirically verified torque-speed curves for both motor modules at 60 V.These actuator limits support the planning and control framework for dynamic aerial motion.
  • Battery model: Battery voltage sag under high power draw is incorporated into actuator limits, with voltage constrained against dropping below 50% of the fully charged state.The estimated voltage is combined with torque-speed calculations to determine actuator limits at every simulation timestep.

III. PLANNING AND CONTROL

The framework divides aerial motion into takeoff, flight, and landing, assigning specialized planning and control methods to each phase. AAKD plans takeoff, PD control tracks flight configurations, and MPC with whole-body impulse control stabilizes landing and other high-rotation phases.

  • Framework overview: Dynamic aerial motions are divided into takeoff, flight, and landing phases with phase-specific planning and control.The framework combines AAKD, PD control, MPC, and whole-body impulse control.
  • Takeoff: AAKD selects the required motion and optimizes a centroidal-dynamics trajectory that achieves it feasibly.Example selected motions include jumping onto a table and performing a backflip.
  • Flight: During flight, robot joints use PD control to track a configuration determined by the AAKD planner.
  • Landing: During landing, QP-based MPC plans reaction-force profiles to stabilize the robot as it contacts the ground.
  • Whole-body control: A whole-body impulse controller realizes planned takeoff and landing motions while stabilizing motions with large rotational components.

A. Kino-Dynamic Planning

The kino-dynamic planner optimizes full-body and centroidal trajectories while enforcing kinematic, dynamic, contact, and actuator-related feasibility. Its actuator-aware approximation maps dominant reaction-force effects to configuration-dependent joint-torque limits without retaining the full nonlinear relationship.

  • Optimization variables: The optimization includes trajectories for generalized states, center-of-mass motion, centroidal angular momentum, contact points, and ground-reaction forces.All trajectories are discretized across timesteps and condensed into one optimization variable.
  • Motion selection: The motion selector supplies a reference motion and allowable terminal states, while the terminal condition enforces the desired final motion.The reference guides optimization through an objective weighted by Q_X.
  • Feasibility constraints: Centroidal dynamics, timestep continuity, joint ranges, and kinematic agreement constraints enforce dynamic and kinematic feasibility.Continuity is imposed using backward Euler integration.
  • Contact constraints: Contact constraints distinguish limbs in contact from limbs out of contact and impose corresponding ground and friction conditions.The contact schedule is specified before optimization.
  • Actuator awareness: Actuator-limit constraints are included because reaction-force penalties or maximum-force constraints alone are insufficient for hardware-pushing acrobatic motions.
  • Torque approximation: Joint torque requirements are approximated from dominant reaction-force terms, then contact Jacobians are linearized around reference positions for selected joints.The approximation reduces nonlinear dependence on robot configuration while retaining hip-flexion and knee dependence.

B. Landing Model-Predictive Control

The landing controller uses MPC with a simplified lumped-mass model for long-horizon optimization, connected to WBIC for high-bandwidth feedback and impact dissipation. The formulation simplifies body orientation and rotational dynamics to support real-time optimization.

  • MPC and WBIC are combined to dissipate landing kinetic energy while responding rapidly to modeling errors and disturbances.MPC handles long-sequence optimization, while WBIC provides high-bandwidth feedback control.
  • The MPC uses a simplified lumped-mass model and linear time-invariant dynamics to speed optimization.The formulation assumes body orientation changes little over the MPC horizon and represents orientation with Euler angles.
  • The angular-velocity approximation retains one dominant principal-axis rotation while neglecting precession and nutation effects.Pitch dominates back/front flips, whereas yaw dominates 180° turning jumps.
  • The MPC discretizes the simplified dynamics and minimizes reaction forces together with state-reference error over the horizon.The optimization is constrained by dynamics, initial conditions, and ground-reaction-force limits.
  • The landing MPC uses a 0.1 s timestep and a 15-step horizon, optimizing 1.5 s of future state.The desired center-of-mass position is based on the four foot-contact locations, with a landing height offset of 0.05 m.

C. Task Setup of Whole-Body Impulse Control

The WBIC landing setup resolves orientation and task-priority issues arising when MPC’s lumped-mass reference is transferred to the humanoid. Body orientation is prioritized, while lower-priority centroidal-momentum and posture tasks support balance and emergent arm motion.

  • WBIC accepts MPC reference reaction forces and optimal motion while providing whole-body feedback for landing control.This extends the framework beyond sharing only MPC position commands.
  • The humanoid body orientation approximates lumped-mass orientation because most mass is concentrated in the body and dominant actuators move little.This approximation makes the MPC orientation reference usable as a WBIC body-orientation task.
  • Body orientation is prioritized above the centroidal-momentum task because rotating the body can support long-term balance.The centroidal-momentum feedback tracks centroidal angular velocity without orientation-error correction.
  • The centroidal-momentum Jacobian is chosen to represent centroidal-motion control rather than inertia shaping.The Jacobian is defined as J_CM = I^-1 C_M A_CM.
  • Lower-priority posture tasks projected into the centroidal-momentum null space automatically generate arm motions that counteract body-orientation control.These emergent arm motions reflect the controller’s CAM-minimization intent.

IV. RESULTS

Simulation experiments demonstrate acrobatic humanoid motions using actuator-aware planning, whole-body control, and actuator-detailed dynamics. The AAKD planner respects actuator limits while adding limited solve-time overhead, and the demonstrations remain simulation-only.

  • The custom simulator models rotor inertia, torque-speed relationships, and battery voltage droop alongside the humanoid’s rigid-body dynamics.These actuator effects are included to reflect hardware behavior during simulation.
  • AAKD respects actuator limits for a 180° spinning jump, whereas standard kino-dynamic planning does not in the reported worst-case approximation.The comparison involves large hip-yaw and hip-abduction/adduction displacements.
  • AAKD coordinates high-speed center-of-mass propulsion with angular-momentum generation about principal axes to produce flips and spins.The demonstrated motions include a 180° spinning jump and a standing front flip.
  • WBIC tracks takeoff and landing motions, accounts for model errors, and recovers from small perturbations while obeying actuator limits.The standing front flip is treated as a worst-case motion because of its substantial rotation and severe ground impact.
  • The acrobatic demonstrations are strictly simulation results, despite actuator models calibrated against experimentally verified torque-speed behavior and battery limits.Remaining assumptions concern inertial properties, rigid ground contact, and adequate state estimation.

V. CONCLUSIONS

The paper concludes with a system design combining a new humanoid, actuator-aware motion planning, and landing control for acrobatic motion. Two new actuators and dynamically consistent MPC-WBIC integration support feasible simulated trajectories with actuator-model verification.

  • The proposed system design combines a new humanoid robot, motion planner, and landing controller for acrobatic motion.
  • Two new actuators meet torque and power requirements for impulsive behaviors.
  • The planner adds a torque-limit constraint to a simplified kino-dynamic model, while simulation verifies actuator outputs using torque-speed, battery-droop, and back-EMF effects.
  • Landing control integrates MPC and WBIC with dynamically consistent transfer of MPC output to WBIC orientation control.
Loading 2104.09025v1…