diff --git a/wpimath/src/main/java/edu/wpi/first/math/trajectory/TrapezoidProfile.java b/wpimath/src/main/java/edu/wpi/first/math/trajectory/TrapezoidProfile.java
index 7e7bbdcff8..c94f28ba13 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/trajectory/TrapezoidProfile.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/trajectory/TrapezoidProfile.java
@@ -60,10 +60,14 @@ public class TrapezoidProfile {
     /**
      * Constructs constraints for a TrapezoidProfile.
      *
-     * @param maxVelocity maximum velocity
-     * @param maxAcceleration maximum acceleration
+     * @param maxVelocity Maximum velocity, must be non-negative.
+     * @param maxAcceleration Maximum acceleration, must be non-negative.
      */
     public Constraints(double maxVelocity, double maxAcceleration) {
+      if (maxVelocity < 0.0 || maxAcceleration < 0.0) {
+        throw new IllegalArgumentException("Constraints must be non-negative");
+      }
+
       this.maxVelocity = maxVelocity;
       this.maxAcceleration = maxAcceleration;
       MathSharedStore.reportUsage(MathUsageId.kTrajectory_TrapezoidProfile, 1);
@@ -128,8 +132,8 @@ public class TrapezoidProfile {
     m_current = direct(current);
     goal = direct(goal);
 
-    if (m_current.velocity > m_constraints.maxVelocity) {
-      m_current.velocity = m_constraints.maxVelocity;
+    if (Math.abs(m_current.velocity) > m_constraints.maxVelocity) {
+      m_current.velocity = Math.copySign(m_constraints.maxVelocity, m_current.velocity);
     }
 
     // Deal with a possibly truncated motion profile (with nonzero initial or
diff --git a/wpimath/src/main/native/include/frc/trajectory/TrapezoidProfile.h b/wpimath/src/main/native/include/frc/trajectory/TrapezoidProfile.h
index 72224fda83..13ded46214 100644
--- a/wpimath/src/main/native/include/frc/trajectory/TrapezoidProfile.h
+++ b/wpimath/src/main/native/include/frc/trajectory/TrapezoidProfile.h
@@ -77,8 +77,8 @@ class TrapezoidProfile {
     /**
      * Constructs constraints for a Trapezoid Profile.
      *
-     * @param maxVelocity Maximum velocity.
-     * @param maxAcceleration Maximum acceleration.
+     * @param maxVelocity Maximum velocity, must be non-negative.
+     * @param maxAcceleration Maximum acceleration, must be non-negative.
      */
     constexpr Constraints(Velocity_t maxVelocity,
                           Acceleration_t maxAcceleration)
@@ -87,6 +87,10 @@ class TrapezoidProfile {
         wpi::math::MathSharedStore::ReportUsage(
             wpi::math::MathUsageId::kTrajectory_TrapezoidProfile, 1);
       }
+
+      if (maxVelocity < Velocity_t{0} || maxAcceleration < Acceleration_t{0}) {
+        throw std::domain_error("Constraints must be non-negative");
+      }
     }
   };
 
@@ -131,8 +135,9 @@ class TrapezoidProfile {
     m_direction = ShouldFlipAcceleration(current, goal) ? -1 : 1;
     m_current = Direct(current);
     goal = Direct(goal);
-    if (m_current.velocity > m_constraints.maxVelocity) {
-      m_current.velocity = m_constraints.maxVelocity;
+    if (units::math::abs(m_current.velocity) > m_constraints.maxVelocity) {
+      m_current.velocity =
+          units::math::copysign(m_constraints.maxVelocity, m_current.velocity);
     }
 
     // Deal with a possibly truncated motion profile (with nonzero initial or
diff --git a/wpimath/src/test/java/edu/wpi/first/math/trajectory/TrapezoidProfileTest.java b/wpimath/src/test/java/edu/wpi/first/math/trajectory/TrapezoidProfileTest.java
index 72b730420f..82661295c1 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/trajectory/TrapezoidProfileTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/trajectory/TrapezoidProfileTest.java
@@ -253,4 +253,46 @@ class TrapezoidProfileTest {
     assertNear(profile.timeLeftUntil(0), 0, 1e-10);
     assertNear(profile.totalTime(), 0, 1e-10);
   }
+
+  @Test
+  void initialVelocityConstraints() {
+    TrapezoidProfile.Constraints constraints = new TrapezoidProfile.Constraints(0.75, 0.75);
+    TrapezoidProfile.State goal = new TrapezoidProfile.State(10, 0);
+    TrapezoidProfile.State state = new TrapezoidProfile.State(0, -10);
+
+    TrapezoidProfile profile = new TrapezoidProfile(constraints);
+
+    for (int i = 0; i < 200; ++i) {
+      state = profile.calculate(kDt, state, goal);
+      assertLessThanOrEquals(Math.abs(state.velocity), Math.abs(constraints.maxVelocity));
+    }
+  }
+
+  @Test
+  void goalVelocityConstraints() {
+    TrapezoidProfile.Constraints constraints = new TrapezoidProfile.Constraints(0.75, 0.75);
+    TrapezoidProfile.State goal = new TrapezoidProfile.State(10, 5);
+    TrapezoidProfile.State state = new TrapezoidProfile.State(0, 0.75);
+
+    TrapezoidProfile profile = new TrapezoidProfile(constraints);
+
+    for (int i = 0; i < 200; ++i) {
+      state = profile.calculate(kDt, state, goal);
+      assertLessThanOrEquals(Math.abs(state.velocity), Math.abs(constraints.maxVelocity));
+    }
+  }
+
+  @Test
+  void negativeGoalVelocityConstraints() {
+    TrapezoidProfile.Constraints constraints = new TrapezoidProfile.Constraints(0.75, 0.75);
+    TrapezoidProfile.State goal = new TrapezoidProfile.State(10, -5);
+    TrapezoidProfile.State state = new TrapezoidProfile.State(0, 0.75);
+
+    TrapezoidProfile profile = new TrapezoidProfile(constraints);
+
+    for (int i = 0; i < 200; ++i) {
+      state = profile.calculate(kDt, state, goal);
+      assertLessThanOrEquals(Math.abs(state.velocity), Math.abs(constraints.maxVelocity));
+    }
+  }
 }
diff --git a/wpimath/src/test/native/cpp/trajectory/TrapezoidProfileTest.cpp b/wpimath/src/test/native/cpp/trajectory/TrapezoidProfileTest.cpp
index e83da634b6..0846e8b74c 100644
--- a/wpimath/src/test/native/cpp/trajectory/TrapezoidProfileTest.cpp
+++ b/wpimath/src/test/native/cpp/trajectory/TrapezoidProfileTest.cpp
@@ -241,3 +241,48 @@ TEST(TrapezoidProfileTest, InitalizationOfCurrentState) {
   EXPECT_NEAR_UNITS(profile.TimeLeftUntil(0_m), 0_s, 1e-10_s);
   EXPECT_NEAR_UNITS(profile.TotalTime(), 0_s, 1e-10_s);
 }
+
+TEST(TrapezoidProfileTest, InitialVelocityConstraints) {
+  frc::TrapezoidProfile<units::meter>::Constraints constraints{0.75_mps,
+                                                               0.75_mps_sq};
+  frc::TrapezoidProfile<units::meter>::State goal{10_m, 0_mps};
+  frc::TrapezoidProfile<units::meter>::State state{0_m, -10_mps};
+
+  frc::TrapezoidProfile<units::meter> profile{constraints};
+
+  for (int i = 0; i < 200; ++i) {
+    state = profile.Calculate(kDt, state, goal);
+    EXPECT_LE(units::math::abs(state.velocity),
+              units::math::abs(constraints.maxVelocity));
+  }
+}
+
+TEST(TrapezoidProfileTest, GoalVelocityConstraints) {
+  frc::TrapezoidProfile<units::meter>::Constraints constraints{0.75_mps,
+                                                               0.75_mps_sq};
+  frc::TrapezoidProfile<units::meter>::State goal{10_m, 5_mps};
+  frc::TrapezoidProfile<units::meter>::State state{0_m, 0.75_mps};
+
+  frc::TrapezoidProfile<units::meter> profile{constraints};
+
+  for (int i = 0; i < 200; ++i) {
+    state = profile.Calculate(kDt, state, goal);
+    EXPECT_LE(units::math::abs(state.velocity),
+              units::math::abs(constraints.maxVelocity));
+  }
+}
+
+TEST(TrapezoidProfileTest, NegativeGoalVelocityConstraints) {
+  frc::TrapezoidProfile<units::meter>::Constraints constraints{0.75_mps,
+                                                               0.75_mps_sq};
+  frc::TrapezoidProfile<units::meter>::State goal{10_m, -5_mps};
+  frc::TrapezoidProfile<units::meter>::State state{0_m, 0.75_mps};
+
+  frc::TrapezoidProfile<units::meter> profile{constraints};
+
+  for (int i = 0; i < 200; ++i) {
+    state = profile.Calculate(kDt, state, goal);
+    EXPECT_LE(units::math::abs(state.velocity),
+              units::math::abs(constraints.maxVelocity));
+  }
+}