[Paper Review] A Whole-Body Model Predictive Control Scheme Including External Contact Forces and CoM Height Variations

Reihaneh Mirjalili, Aghil Yousefi‐Koma+4 more|arXiv (Cornell University)|Oct 24, 2018

Robotic Locomotion and Control13 references4 citations

TL;DR

This paper proposes a three-stage Model Predictive Control (MPC) scheme for humanoid robots that jointly plans whole-body motion, Center of Mass (CoM) height variations, and external contact forces (e.g., hand contacts) in real time. By decomposing the problem into convex Quadratic Programs (QP) and a Mixed-Integer Quadratic Program (MIQP), the method enables reactive, physically feasible whole-body motions on uneven terrain or with object manipulation, overcoming limitations of the standard Linear Inverted Pendulum Model (LIPM).

ABSTRACT

In this paper, we present an approach for generating a variety of whole-body motions for a humanoid robot. We extend the available Model Predictive Control (MPC) approaches for walking on flat terrain to plan for both vertical motion of the Center of Mass (CoM) and external contact forces consistent with a given task. The optimization problem is comprised of three stages, i. e. the CoM vertical motion, joint angles, and contact forces planning. The choice of external contact (e. g. hand contact with the object or environment) among all available locations and the appropriate time to reach and maintain a contact are all computed automatically within the algorithm. The presented algorithm benefits from the simplicity of the Linear Inverted Pendulum Model (LIPM), while it overcomes the common limitations of this model and enables us to generate a variety of whole-body motions through external contacts. Simulation and experimental implementation of several whole-body actions in multi-contact scenarios on a humanoid robot show the capability of the proposed algorithm.

Motivation & Objective

• Address the lack of reactive, multi-contact motion planning in humanoid robots during dynamic disturbances, as observed in the DARPA Robotics Challenge.
• Overcome the limitations of the Linear Inverted Pendulum Model (LIPM), which assumes constant CoM height and no external contacts.
• Enable automatic selection of contact locations and timing for hands or other limbs to maintain balance and achieve tasks.
• Develop a computationally efficient, real-time capable motion generation framework suitable for complex, dynamic environments.
• Bridge the gap between high-dimensional non-convex optimization and reactive, low-complexity planners by decomposing the problem into convex subproblems.

Proposed method

• Decompose whole-body motion planning into three sequential convex optimization stages: CoM vertical motion, joint trajectory, and contact force/selection planning.
• Use a Quadratic Program (QP) in the first stage to generate a feasible CoM height trajectory within kinematic bounds, considering reachability and stability.
• Apply a second QP to compute joint angles and whole-body motion while satisfying ZMP (Zero Moment Point) and kinematic constraints.
• Employ a Mixed-Integer Quadratic Program (MIQP) in the third stage to automatically select optimal contact locations (e.g., hand contact) and contact forces.
• Integrate contact timing and force decisions into the MPC loop, enabling dynamic contact switching in response to task and stability requirements.
• Use the ZMP constraint and physical limits (e.g., joint angles, reachability) as hard constraints in each optimization stage to ensure feasibility.

Experimental results

Research questions

• RQ1 Can a real-time MPC framework automatically plan both CoM height variations and external contact forces for humanoid robots in dynamic scenarios?
• RQ2 How can the computational complexity of multi-contact motion planning be reduced while maintaining generality and physical feasibility?
• RQ3 To what extent can the proposed method overcome the simplifying assumptions of the LIPM, such as constant CoM height and no external contacts?
• RQ4 Can the algorithm autonomously determine when and where to establish or break a contact (e.g., hand contact) during motion execution?
• RQ5 How does the integration of CoM height control improve the robot’s ability to perform tasks like lifting objects or navigating uneven terrain?

Key findings

• The algorithm successfully plans smooth, physically feasible CoM height trajectories within kinematically admissible bounds, as demonstrated in box-lifting scenarios.
• The third-stage MIQP automatically selects optimal contact locations and forces, enabling the robot to maintain balance when CoM motion would otherwise violate ZMP constraints.
• In multi-contact scenarios, such as passing through a hole or making large lateral steps, the algorithm autonomously determines contact timing and locations without pre-specification.
• The method enables stable whole-body motions on uneven terrain or during object manipulation by dynamically adjusting CoM height and contact forces.
• The decomposition into convex QPs and MIQP allows real-time execution, with each stage solving efficiently at control cycle frequency.
• The algorithm maintains robustness by incorporating joint limits and reachability constraints, preventing infeasible motions even under dynamic task demands.