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Model Predictive Control (MPC) – A Review

The Model Predictive Control (MPC) approach is a powerful technique for controlling legged robots, particularly those with complex dynamics. It involves predicting the future behavior of the robot over a specified time horizon and then optimizing control actions to minimize a cost function that typically includes tracking errors and constraint violations.

At its core, MPC utilizes a dynamic model of the robot – often derived from Newton-Euler equations – to predict its state at future time steps. This prediction is combined with a cost function that penalizes deviations from desired trajectories and adherence to constraints such as joint limits and obstacle avoidance. The optimization problem solved by the MPC controller generates optimal control actions for each time step, based on this predicted behavior.

The key advantage of MPC lies in its ability to explicitly handle constraints. Unlike traditional PID controllers which often struggle with complex constraint interactions, MPC can incorporate these constraints directly into the optimization process, ensuring that the robot’s movements remain within safe operating limits. This is particularly crucial for legged robots, where maintaining stability and avoiding collisions are paramount.

Furthermore, MPC allows for adaptive control strategies. The model itself can be updated as more data becomes available, improving the accuracy of predictions and allowing the controller to adapt to changing conditions such as variations in terrain or payload. Advanced MPC implementations may even incorporate learning algorithms to further refine the model and optimization strategy over time.

Model Predictive Control (MPC)

The MPC approach involves solving a quadratic program (QP) at each time step to determine the optimal control inputs for the robot. This QP considers the current state of the robot, its dynamics, and any constraints on its motion.

Warm starting is used to speed up the solution process by using the previous solution as an initial guess for the next iteration. The solver then refines this solution based on the new state information.

Real-time solvers are employed on embedded hardware to enable the MPC controller to operate in real-time, allowing the robot to respond quickly to changes in its environment.

Examples

Example: Stair Climbing MPC

Plan footholds from perception.

Optimize CoM and contact forces under constraints.

Test robustness with disturbances.

Frequently asked questions

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